the highest possible is a Athlon 3700+ at 89w, which of course depends on whether your board actually goes up to that, and if not, whether there's a bios update for it. And yes, there is a difference in pin numbers and wattage. This is assumption as you did not provide with the board manufacturer and model number, thus, served as a guide only.
As for shutting down, a few possible reasons, one being the fan cooling the processor is not contacting properly or overclocking without properly cooled or memory module issues (ram bus speed is actually not meeting the minimum speed). Another could be software which you last installed giving this problem. These are some in which you could look into. Most important is tracing the problem, or even getting a new processor may not solve the actual underlying problem at all. Hope it helps.
Among all the other options I am thinking of, I am considering replacing my CPU to solve a problem of the computer just shutting down for no good reason. I can't isolate it to a heat problem, it can happen shortly after I boot up or a long time after, sometime it will just keep happening and sometimes it just happens once. I actually bought a system that is going back because it doesn't work and my system I built way back, I am thinking I feel better with something I know about. On Ebay they have some direct replacements, but I am thinking if I go through all the bother of replacing it, I want something a little better. Most of the better AMD 64 that are faster are Socket 939, I am not sure, but I think that is the number of pins? Does anyone know what is the maximum upgrade I can use for a Socket 754?