Hey Kharris,
As far as i know the battery is only for the clock - but the board will still boot up without it. I shouldn't have mentioned the restart loop... it's hard to determine without an oscilloscope or logic analyzer, and if it's happening then your board is dead anyway.
At this point I would isolate the board from everything else and see if it behaves the same... If you disconnect everything from the board (maybe take a picture first), connect only the 10/18/24vac transformer connector, and power it up... the board should boot and at least let you into the menu system. If it doesn't, then either the power supply or the board is bad.
Even though the input is marked 10vac, you can power the board with a 12vdc wall-wart that can supply at least 600mA. I do that on my bench, and Pentair does it with their trainer systems. if you want to try it, see my 8/3 post in this thread for the correct polarity:
Easytouch Questions
Hopefully your transformer is just not supplying enough power - these things will restart and/or act all manner of crazy if they don't get enough juice.