I had one of these up until this year (The 2.66ghz) and they can be extremely finicky, I believe you could use almost any logic board, thats made for this specific body style of mac pro(Before 2008 revision), but make sure your Xeon's will fit the board you get.
Personally, I don't really think the logic board would have failed for no reason.
I could be wrong though. Tearing out the logic board will be a long grueling process... My friend had one that need a board, and we opted to sell it over, beginning that process.
I am leaning toward the power supply. I'll look around this evening and see what I can figure out. This 06 Mac Pro has alot of life left in it, and it can be fixed. This was a very expensive machine when it was new.
What gpu are you running? As a long shot the graphics card may have failed.
I will do some research and get back to you, I am done w/ classes in the next couple weeks, I am completely down to help you diagnose exactly what has failed. Once you know whats wrong, the rest is easy.