Dying Floating Plants

So, hello everyone.

I have an 8 gallon biocube which I bought because of a deal and it seemed that having everything inside it, the lights and the filter all together, was nice. I kind of regret it now and wish I had just gotten a normal tank (as this one has plastic sides which get scratched, the small size, the predetermined layout, etc)

This is the first aquarium I've had since I was a child, so really, the first aquarium I am taking care of on my own. I am interested in putting shrimp in it, red cherry shrimp, which I hope to buy soon. I've had the tank for a few months now, about three, and I believe it's cycled and everything. The only animal I have put into it was a malaysian trumpet snail (which is now several) and they seem to be doing fine. I put some plants in there from petsmart, but I made the new mistake of buying the ones in tubes, which I have learned are not aquarium plants at all. There are now an aponogeton bulb and a water onion bulb, the only two to sprout out of three packs of those dried bulbs.

That's just a breif history of my tank.

I went to my local fish store a couple weeks ago and got some duckweed for free, because I liked how it looked and liked floating plants. I thought it was charming. So I put that in and it seemed to grow and reproduce.. for about a week. A big patch of it started dying near the filter side of the tank. There was a strange white substance around the roots, probably due to decaying roots, and the leaves were clear and whitish, not yellow. I scooped out a bit of it, including some healthy plants in case it was infectious. A few days later, all of the plants (or a large portion, but mixed in with the good) were looking the same way. I scooped it all out and tried to figure out what was up, but I guessed it was just some kind of incompatability with my tank and the lfs tank.

Now, I bought some red root floater plants from a user on here (Right now saying I doubt that this has anything to do at all with his aquarium ability) probably against better judgement, but they weren't expensive and if they did grow I'd be happy with them. They were doing fine for almost a week, sprouting new leaves, all of them. Then I look in this morning, and same symptoms as the duckweed. A small clump near the filter looking clear and sickly. I stirred up the plants, so I could see if it's something with the filter. When I come home from work or tomorrow morning, the plants should look sickly by the filter. I should have taken a picture, but I will tonight if I can get an obvious patch.

I do not know what the problem is, is it possibly a lack of nutrients? In which case, I am willing to just forget about floating plants entirely. If it is a problem with my water, I would like to figure it out before putting shrimp in. If it is a problem with lighting, I would like to fix it, but the nature of the biocube would probably make this difficult. If it is indeed a problem with the filter, maybe I should look into that as well, but again..biocube.

Anyway, sorry for the long-winded post, and thank you for your help.

Thanks for the responses. No, I'm not using a UV filter, and my surface water is fairly still, I moved the head so that it didn't push the surface too much, I've noticed I have a oily layer on top (probably from my skin when handling things), and the plants closest to the filter output were fine, it was the input ones dying. It's probably a lack of nutrients.. I don't put much into the tank as there is enough algae for the snails to eat and I have nothing else to feed, so there probably isn't much of anything for the floaters to draw out of the water. Considering I got enough of them to cover the whole top of the aquarium, it's probably too much, so they're all getting sickly. I'm going to try and take out most of it and find the healthiest looking ones and leave them inside. Maybe it's just too much for my tank.

In the attached picture you can see some of the worst of the plants, as well as the oil on top.