I had one of those...
I had a Fluval 303, just broke down that tank and sold it in fact.
So, hmm, how to begin? If the unit is running, warm, but no water is coming out, then the impeller may be broken, the impeller cover may be broken, or the motor may be shot, or there may be a bubble in the input line which lost the siphon (most likely but once siphon is lost the motor can burn out too).
First look at the line from the tank going into the filter, any bubbles? If so that is probably it, and you can backwash the line which may be all you need to do to fix it if there is a bubble. To do that, turn power off, then close all valves. Unhook the input line (from tank into filter), take a bucket and open the valve and shoot water into the bucket until that bubble is blown out. This may be enough to fix it. Replace everything and plug it in, see if that worked, but when you reconnect a new bubble may rise from the canister into that line again. You may have to bleed water through the filter out the outlet of the filter to blow all air out the entire assembly. But, for now, just reconnect and see if you get lucky and it restarts OK. Or continue with a cleaning, which is really a good idea at this point.
Unplug power and close all valves, pay attention to the little diagrams on the valves to see what is open and what is closed. Turn the nut with hand or wrench and pull the two pieces apart. Have a towel handy, one on the floor and one on your shoulder. Have a big bucket handy also, in case you screw up and need to catch a lot of water!
I wonder is the cansiter on yours brown or black? The brown one seems more delicate and I had one that had broken at the clips, so be careful.
Be sure the valve attached to the hoses that go to the tank are securely closed, leave a big towel there, then take the canister to a sink or tub.
Also, with that big bucket, find the outlet tube going from the filter back to the tank, and open the valve and shoot water into the bucket, about 1/2 full, then close the valve. Keep that towel handy. Take the bucket to the sink or tub with the filter. Yes, that water is a bit dirty but that's OK. You did a good thing backwashing the tubing and that crud would have otherwise shot into the tank when you restarted the filter.
Now, you will take the filter apart. First, open the valves on the tubings. This lets air into the canister so the vacuum is broken, no use working against the vacuum. Open the clips, pry the top off. Keep track of the O-ring, put it in a safe place -- vital part.
Now take the media baskets out, twist to separate them and rinse the media in the bucket of water you took from the tank. Yes, I know the bucket is full of rather dirty water already, but you can get more. Dunk swish or even pour into a colander (do clean it well before you return this colander to the kitchen however)
Rinse the sponges, the media, everything off in the tank water. Get more if needed, dump the nasty water on house plants, they love it. It is OK to drain from the tubing that returns water from the filter to the tank until it runs dry if you need that much water. Use the other tubing if you need to as well,if you had a bubble that broke the siphon you will blow it out doing this.
Now, take a moment to look at how the hoses are connected to the valves and the filter head. There is a nut that goes one way to expose a barb that is stuck into the tubing, then goes the other way to tighten against that barb to hold the tubing. The tubing needs to have a nice smooth edge on it to be held correctly and if the tubing is bent close to that connection it can come loose (so be careful moving that filter around, done that too). At some point you will need to check that connection on the tubings that are still attached to the tank, but not today. Let's just do this for now.
OK, now the media is clean I guess. Let's look at the impeller. Opening the impeller cover is tricky and it is all too easy to break it. I have no real advice here, I broke two on the same day. One was in use, the other on the old filter with the broken canister clips was a backup. Broke one, then the other trying to get it off the spare to replace the one I broke. Replacement is cheap, $4 online plus $7 shipping but takes a week to arrive. Better yet, let me suggest you order one now and if you may want to test to see if it works OK, don't try to open it to clean it today. If you found a bubble on the input line skip this until you feel you need to do this test, sort of advanced investigation and probably not necessary unless everything else does not work.
Testing the operation of the motor and impeller; Take the filter head, just the top of the filter, to the tub and fill to about 2" deep. Hold the head so that it is in the water but not under the water, plug the unit in (yes this is tricky, you probably need help here). I suggest doing this in the bathtub, for if the impeller works, it will pump water out the open valves onto the wall or onto you or your help, so aim carefully! If it does not pump, or spits once and quits, you have a problem. That problem may be the cover or the impeller itself. If it does pump well, you might just skip cleaning the impeller until you have a replacement cover. Your choice.
Cleaning the impeller; When you clean it, you need a filter brush set so order that online also. You will take the cover off carefully, it sticks badly. Remove the impeller and brush totally clean, OK to use tap water, brush inside the impeller well (the hole) being careful to see that the rubber bushing on each end of the shaft is accounted for. The one inside the impeller well may get stuck and you can leave it there, but be careful when you put the thing back together that you get the shaft into that bushing. Put the cover back on and lock into place. The shaft is delicate and the impeller assembly is very exxpensive.
Now, with the media clean, the impeller cleaned (or not, this time) and the tubing at least partly cleaned from shooting water through it when you drained water through it, you are ready to put it all back together.
Put the O-ring on the filter head, it is a bear sometimes. Get it in place and be sure it is not ready to pop off. Push it down well and untwist it. Put the baskets back together, sponges in the top basket, and then put the whole assembly into the clean canister. With the valves open you should easily slip the head onto the canister. Close clips.
OK, now hopefully the tubing that goes to the input side of the filter is still full of water, no air bubbles at all. Look at the tubing to be sure, if there is a bubble it will be at the bend at the top and it will have lost the prime on the siphon. If you see one, open that valve and shoot water into the bucket until you blow that bubble out. If you saw a bubble here at the start, this may have been all you needed to do to fix things, but it is worth the time to do the cleaning.
Before you go any further, be sure you know which is the input and the output lines and you know which goes where on the filter head. If you hook them up wrong, nothing you do can make it work (done that too)
Hook up the input line to the filter, keep the tank side valve closed. Be sure it is OK, tug on it, sometimes it feels locked but isn't. Now you have a choice to either start the water now and then hook up the second tubing to the tank which, if you have trouble will mean water on the floor and on you, or hook it up first, test the connection, and then open the valves but this sometimes does not work as well and you have to undo everything and start over after you dump the water from the canister, or else find the input at the tank and find a way to suck on it. For a long time, I put the filter into the big bucket and opened the input valve and as the filter was filling with water I worked on attaching the output lines (if you do that be sure that both output valves are open), often I ended up with water spewing out the output side of the filter before I had it all connected -- as awkward as this sounds it actually worked better than almost anything else, for all air was out of the canister and none could rise up the input line and break the siphon. The other way is to hook it all up and just hope that no bubble drifts up the input. I think letting water shoot out the filter works best, if you can stand it. As a last resort, you can attach a hose to the output inside the tank and suck on this to get water moving, but I absolutely hate getting tank water in my mouth. Water in the bucket works for me. (Can you see why I sold it??)
Anyhow, once you get the thing all hooked up and plug it in, you probably need to gently shake it to get the bubbles out of the unit. Be gentle, for you don't want to break that tubing connection (done that, what a mess)
When my 303 was running it was great, silent, perfect. But after a cleaning it was such a pain to get restarted, in part because I made so many mistakes, connecting the hoses wrong, trying to open or close the canister with the valves sealed, tipping it too hard trying to get the bubble out of it after it started and pulling the hose connections off, and the constant battle with that little bubble drifting up the input line after I reconnected it all.