iMac G4 flat panel won't stay powered on

I have an imac g4 15" flat panel that started to unexpectedly power down when I was listening to music on iTunes. I could turn it back on manually with a bit of persistance and then finally it just wouldn't turn on anymore. I did a bit of research and found out about the PMU reset and tried that. The
computer did start up after this reset but then powered down again after about 15 minutes and is dead again.

I have no experience disassembling computers but am mechanically
inclined. I have obtained the service manual for the computer and according to the research that I have been doing, I am going to follow these steps one by one to try and resolve my problem.

1. replace the ac adaptor/power cord - the original has been quite abused
2. try resetting the PMU with the new power cord
3. Zap the PRAM
3. replace the PRAM battery
4. replace the power supply

Does this sound like a logical chain of troubleshooting? Do you have
any suggestions where to purchase the supplies/parts that I need?

I'd start with the cheapest means first, like stuff like resetting the PRAM and other things to check for hardware issues first.
If the cord is bad, replace it. I wouldn't be messing around with cut cords and such. You can pick up a new one for a few bucks.
It all sounds good to me.
Bryan

I had the same problems that you have listed, but mine happened over a week. I'd come home and my computer wouldn't be on. I could turn it on and then it would be fine. However, it would turn itself off constantly. If you open up the back of the case, my power supply was the culprit and it left a smokey-esque mark all over the back of the inside.

i would definately check the cheaper parts like mentioned already, also make sure the fans are running

With all the Macs I have owned and worked on, the PRAM battery can cause it not to power on, but have never seen it just shut off like that once it was booted. I would still check the battery when you are in there.