I have an Acer Aspire 5520 in my house that doesn't boot, but I never bothered to look around and try to fix until today.

Basically, here's what happens:
1. Press the ON button
2. Nothing happens (no sound, no light, no beep, no reaction at all!)

I tried doing this either using AC Power and Battery Power, and AC Power with Battery removed too.

When it has the battery inside and the cable is connected, the Battery LED (meaning it's charging) goes red. This is the only thing that works in the computer.

Since it doesn't boot (not even BIOS, as I said nothing), I have absolutely no idea of what to do. Other people online have problems with this computer, but no problem like mine.

If you have any ideas, I'd appreciate them, thanks!

I've had a similar problem before.
My laptop wouldn't start into BIOS at all, but the battery light worked fine.
After a while I realized that a USB mouse I had plugged in was messing up the boot sequence (for whatever reason), and after removing that it worked.
Though if this is a long-time problem I doubt it's a peripheral acting up :\

Hmmm, that sounds like it got overheated
Maybe if you open it and clean all the dust, disconnect the fan (to try temporally, as the fan might  be broken) you will have the luck that is starts again.