The bog standard A1200 PSU gives 23-25W where's the A500 gives 50W. The standard PSU for the A1200 isn't ment to take any upgrades except for HDD and PCMCIA memory. Usually sticking a turbo to it fries it eventually, add an external floppy or two surtanly takes it down sooner or later. I actually fried an A500 PSU with a A1200+3,5" HDD+2 external FDD and a B1230 so that too can be underpowered (had the exact same issues with random reboots every 5sec-10min... esp when the PSU gets warm it starts to fail more frequently than when it's cold).
As you have removed the hardware that made the computer start failing and it still does fail I say the PSU have had it. Suggestion to you, try an A500 PSU and if that works then get hold of an old PC AT PSU and use the powercord from the defective original PSU to create a super PSU.
(Just a heads up here, a 200+W PSU is super but now power loss in the powercable to the computer might get to be a problem if you upgrade wildly and you might have to supply the motherboard with a second powercables form the PSU.)
