yours is Early 2008 "3,1" model
Yes there are now cheaper and better FBDIMMs and 4GB is low.
Maybe your update to 10.8
Maybe your graphic card
maybe you should and dont' have a UPS (900W/1500VA) - systems run better longer and have much fewer issues
might be time to do a clean OS install and not keep using the same system, even if you are very diligant and repair it every time it freezes, used ML Recovery Mode, AND were using Safe Boot Mode after these events on next restart.
Turning off on warm boot? cold boot only? you know that is to me a design issue with the 2008. They shipped with a bug in EFI (they wre the first EFI64 / UEFI 2.x) to resolve a freeze on waking from sleep. Also an SMC firmware update. And firmware for the ATI 2600XT that they shipped with. Always better to skip the "first edition" and with new chips and factory firmware.
Tempermential. They or yours - might want to try - are fine with 10.6.8.
What you have to look for are any PowerPC apps you wre using. Still present from "upgrade over SL in place" rather than clean installing.
Any 3rd party hardware, PCIe cards, external devices and such.
You should definitely do a SMC Reset.
And I would try with a single new hard drive just for the system for testing with 10.6.8 and/or ML.
If you have old original or 4-5 yr old RAM try with just the new RAM.How To Install and Remove Memory Mac Pro2x2GB FBDIMM DDR2 667MHz @ $32
I would leave PSU replacement for last but www.dvwarehoiuse.com does carry those or your usual luck with ebay.