Computer restarts itself randomly

Hi I´m new here and I´m starting with a problem, not a good start...
The problem is that I have my previos computer, with this specs:
Pentium 4 Willamette 1.4GhZ, socket 423
Motherboard: Matsonic MS9007C with Intel 845i chipset I think, codename Brookdale.
1.5 Gb of DIMM SDRAM memory 133mhz
Seagate 40gb harddisk

I know, It isn´t very good actually but I want to use it for some tasks as It can do them well. It was always realiable... until now.
Randomly, the computer restarts itself. I suspected it was a hard disk problem and I formatted and resintalled Windows, zero-filled it to evade bad sectors, a complete format and no luck. I think it can be some memory module or the powersupply. It restarts in every situation: sometimes while Windows is booting, when desktop is loading, when you´re working on it or even if it´s idle. I remember some time ago one of the times I clean the computer interior (9 years the computer has) one of the memory modules wasn´t recognised at start and I had to "play" with it to get it working but after that it didn´t ive me any problem until now. I´m going to dissasembly completely the computer to clean it, inspect it and put some oil on the vents as they are loud with the years.
Any ideas of what can I look for to solve the problem? Memory, hard disk, power supply, everything? Maybe I should take it to the recycle bin and use only my new one computer? heh

Thank you