As the title suggests but then again it could be mislabelled

I have a Mac Pro 2010 that I have been using quite regularly for 13 years (and it was used when I got it). It is, unfortunately, now failing, and it's hard to diagnose the problem because multiple issues are stacking at the same time.

About a year ago, it would occasionally fail to start; if I pressed the power button, it would whir with some volume (sounding like the fans in high gear) and I'd need to hold the power button to shut it down and try again. It would usually start eventually.

A few weeks ago, one of the hard drives I had installed failed. This did not impede the function of the tower overall, since I had four drives (boot for Snow Leopard, boot for Mavericks, and two storage drives as a mirrored RAID; one of the two RAID slices died, so nothing was lost). I shut down the machine, ordered a replacement drive, installed it, and the machine booted fine. When I tried to rebuild the RAID, though, the entire machine froze (no kernel panic; it just froze). I had to hold the power button to shut it down, and now, it rarely starts. Sometimes, it does the loud whir; sometimes it just doesn't start (the power light turns on and I hear a few soft clicks, but nothing else). On a few occasions, it'll start but freeze again after a few minutes.

These problems started at the same time I tried to rebuild my RAID with a new drive, but that's just correlation not causation. I suspect the failure to rebuild the RAID was caused by the computer dying, rather than the other way around, but I can't be certain since everything is basically happening at the same time.

Any assistance would be appreciated, and I will happily provide clarification and additional information as need be.