hmmm a 430w PSU should be perfectly fine for that comp, and your right about the CPU, it could not possibly be overheating THAT quickly. it is my belief that the computer is shutting itself down to avoid damage due to improper connections or faulty hardware. now, the quickest and easiest thing to do first, is to check that everything is connected properly. check each and every cable that is plugged into the motherboard, make sure that they are all plugged into the correct spot according to the motherboards manual. if you cannot find any errors, then we can move on into testing the hardware.
the first piece of hardware i suspect would be your RAM. you say that you have 4gb of DDR2 800, so i can safetly assume that you have at least 2 sticks if not 4. remove all but one stick of RAM. try booting the computer using that one stick of RAM. if the computer boots and stays running, then one or more of the two or three other sticks of RAM is faulty. if your comp dies again, try another stick of RAM, do this for all 2 or 4 if you have to.
please post back if you are confused about any of this or the above advice does not work.