I'd look at that given the age of the system. GOOGLE bad caps to see if you have one or more on your motherboard. Your PSU has them also, can cause a power drop-out under load. PSU's are known to deteriorate in power output rating over time as well. So, a unit rated at 400 watts continuous ten years later can only provide 200.
I built this computer about 10 years ago. I used quality products. Asus MB, WD HDD, lets put it this way. I did my best to use the best. I have replaced the processor and video card. Still when I start up I can get it to the BIOS for maybe 4 or 5 seconds then it shuts down. I have even reformat the HHD. And when I do that I use KILLDISK, I Wipe the HDD clean. So I reinstalled Windows XP PRO.
It then started normal and did the same thing, shut down. I have been working with computers like I said. Don't get it, anyone have an Idea?