My thinking when something needs to stay on for a while for something different/better to happen it's most likely component dammage (solders and other metals expand when getting warm to give a possible better connection or capasitors thats on their last leg and need execive loading time for them to charge).
If I was you I'd stripp down the machine to motherboard alone (rule out other components such as bussboard, hdd/optical drives/floppy etc messing with the machine), make sure all the jumpers are set correctly. If you have a complete teardown in front of you with just motherboard and it still fails on you there's 2 options. Either it's the PSU or it's the motherboard and as you've just removed alot of load of the PSU without any changes occured it's more likely that the acidstained motherboard is actually dammaged (if you like you can always get hold of a second hand PC PSU and convert it to give power to the motherboard if you want to be totaly sure that isn't the culprit).
Remove ALL the acid and corrosion (dry clean is best to start with as water just gets the acid everywhere, then get yourself something that neutralize the acid to wetclean the rest and after that clean all again with regular wather), then inspect the motherboard carefully and repair dammaged/lost lines (and possible components) on the motherboard, don't be shy with the soldering iron.
Good luck. :-D
