I typically decase a CPS2 first, then run it for about 20 minutes, then I power down and do the surgery. I solder a lot, so the process has always gone smooth for me. I think most suicide conditions will be a blue screen, or red or green, whichever.
if you suspect your power supply may be at fault, measure the voltage at the power supply. if your 5 volt line is showing dead that means the power supply is in shutdown. I'm guessing you didn't mess with any of the power wiring, if you were to short one of the voltages it would cause a shutdown.
lots of older power supplies will attract a lot of dirt, particularly the box style units because they have cooling fans and just the moving of the air will cause a lot of dirt buildup. this consequently can also get the +5 adjustment pot dirty, and if the power supply is unable to get a resistance reading off the adjustment pot, it will cause it to shutdown. Peter Chou models are more prone to this for whatever reason, and their box power supplies have terrible fans that seize up.
if you read the PSU guide in my signature I have a portion in there about wiping an adjustment pot. just make sure to have the JAMMA harness unplugged from the board and do a brief power cycle to see if the power supply comes back on. if it does, power down and get your volt meter handy, set the power supply at 5.10V, power down once more, then reconnect the JAMMA harness.
if the game all works again, success. if the power supply goes into shutdown again, you have suspect wiring. if the power supply works, but the game still doesn't, then you probably had something go wrong in the battery replacement process.
as noted, make sure you installed it with the correct polarity. installing it backwards will immediately kill the decryption codes and cause the game to suicide and no longer boot.