you may want to take it out of the tank and make sure it is still all connected properly. what kind of filter is it? the usual hang on back ones have the intake pipes, occasionally that can get knocked a little loose and just needs to be pressed back in place. there might also be a lot of gunk inside and you can clean it out quite easily.
sorry, but the water will NOT turn toxic in ten minutes. in the case of a power outage, 24 hours without filtration should be okay. the problem with turning it on and off is that when you turn it on and it has to pull up the water for the first time, that puts a lot of stress on the filter itself. of course, that can be resolved by adding water in the back of the filter when you turn it on. also, a lot of your good bacteria live in there and will get dried out overnight when the water is gone. that is what may really harm your tank. you could take out the filter cartridge and biowheel if you have one and drop them into your tank (which is what you should do if the power goes out), but that's kind of a major pain to fish it out the next day, and the gunk on the back of the cartridge will just fall off into the water which means that you will need extra filtration to get it all out and keep the water clean.
i think the best bet is just to wait and see if your son eventually gets used to the noise. i keep my water level about an inch or so below where the water comes out of the filter, so all i hear is the waterfall noise. might be more soothing and cover the hum a bit better.