G5 2.7ghz dual won't power on

I noticed my Power Mac G5 dual core 2.7GHz that I use primarily for pro tools had shut itself down overnight. Now it won't power up. No light, clicks or any other signs of life. Tried all the tricks, battery, reset button, etc and nothing worked. I would be simply giving up on the beast and upgrading to a new box, (rather than a costly repair,) however get this, the same machine did the exact same thing about a year ago. I gave up on it then too after trying to similarly fix, but about a month later I was moving my computer station and decided to plug it in, I pushed power and presto, it started right up. It has been running fine without any problem at all, for about a year, that is until this morning when I noticed it had again shut itself down and would not start up.

I am hoping the information about it starting after a long rest will give someone a idea as to what may be causing this to happen again. Any advise will be greatly appreciated.

Thanks!