Mac Pro 4,1 not powering on

I've got a mac pro 4,1 that I've had for about 8 years. I powered it on when I originally purchased it with no problems. Put it in storage when I moved and forgot about it.

A few weeks ago I decided to pull it out and see if I could get it running again for kicks and giggles. It powered on after some cleaning and reseating the ram, was able to access the repair screen. Grabbed my time machine drive and started the process of reinstalling everything. Got about 3/4 through the time machine process and the system shut down. Couldn't restart it but also couldn't find any obvious problems. Unplugged everything, repasted the cpu and gpu (using TG-7), and reinstalled. Still no power on initially but after a week it booted again. Repeat the time machine process, and this time it got slightly past 3/4 before shutting down. The only difference I noted this time was the cpu tray seemed to be pushing a lot of hot air (it didnt the first time).

Decided today after taking the computer out of timeout to try repasting the cpu again with MX-4. Realized I didn't do the northbridge the first time so also did it today. Also noted I didn't fully secure the heatsink initially so corrected that. The problem comes now that I've reinstalled everything. Plugged into power (have tried directly to the wall, a power strip (strip works fine, have several other items still plugged into it and also ran the tower the first two times off said strip), and my UPS. None of these have yielded power to the system again.

I've inspected the whole cpu tray and cant find any burned/blown components to replace, swapped my HD5870 (what was originally providing video out with no problems) to the spare HD5770 with no change, checked the backplane board for any burned/blown components and still nothing. Tried one ram stick at a time, nothing (again, system booted and recognized all 24gb the first two times it booted). My next step (maybe should have been my first) is to replace the button battery and see if it will boot with that. Since pressing the diagnostic buttons on the board doesnt yield anything, that may be the problem. But I don't see how that would shut the whole system down when it was working? My concern is that the PSU itself is failing/has failed and any further steps to make the computer work are pointless.

Does anyone have other ideas for what could be wrong? I will be replacing the battery with a CR2032 tomorrow and see what happens from there.