iMac G4 with odd power problem

Okay, so my G4 has had an issue where if I moved the power cord the computer would turn off. I figured it was a solder point issue that occurred due to the weight of the power cord hanging off of it for the past 5+ years. I fixed something to take the stress off.

Well, as of yesterday it won't come on at all. I have messed with the cord hoping it was loose or something and that didn't work. I got the thing apart today and I don't see any loose electrical connection that I can place the blame on... So I'm stuck. I'm not taking it to be repaired until I know what it is that's causing the problem. Or at least what I can point to and say it's this or that because I know it's not this etc... I've heard about a battery on the logic board that dies and can cause this issue. If that's the case where is it at?

Anyone care to lend a hand? This is my kitchen cookbook and iTunes player so I don't wanna loose it.