(1) What monitor showing? no signal detected? (2) Is it single CPU or double CPU? If it is double CPU then whether using single CPU (on the right side one after removing the left one) or switching the CPU between them (partially, temporarily) solve the problem (rebooting with loud fan spin)? (3) consider CPU tray problems?
Ha..ha..ha..I know this is not funny at all. I have this mac pro early 2008 for more than 6 years and it is still working hard till today. Did you guys check the two small buttom battries that sit quietly on mother/ logic board, usually unseen behind the graphic card? Mostly, this is the main culprit! I had some experiences with the s/s above that being resolved after replacing them with the new one. To be safe, replace them every 2-3 years and check its surface contact for any sign of humidity or oxidation. The 2nd possibility is new inserted RAM or maybe the RAM is death. But this rarely cause the symtoms you describe above. Just check on system information about RAM. Then, this one is not easily solved or tracked. You may have accidentally download/ run incompatible software (software conflict) or deleted the important one. Just think what you have done recently with your Mac and search the culprit one by one.
If you purchase Mac Pro 2010 or 2012 with two processors (2x6=12 cores), I suggest you to upgrade its CPU into Intel Xeon X5690 (3.46GHz),. Till I write down this today, the price of X5690 on ebay is around 400$ for a pair (two) of CPU alone or, around 600$ for a pair of CPU plus kits. This price is not included the service. You can find "how to" instructions on YouTube or other place. You can buy the lowest Mac Pro with 2.4GHz (around 1000-1500 now ) then upgrade its CPU by your self. Don't forget to upgrade its RAM too! But, be careful to choose the right one since many (!) Mac Pro 5.1 is actually the upgraded Mac Pro 2009 (4.1).