Dell Optiplex 755 not booting

Kingfisher73 has already helped me with this problem, and I am very grateful to him, but I thought I would throw it open to a wider audience to see if anyone has had similar issues and can help.

I am fairly computer literate and have built several PCs but my son in law got the above for my grandaughter. It had Vista then latterly XP running on it and it was excellent.

Just before Xmas they switched off and 5 days ago they tried to switch back on but kept getting error messages. I took the PC away with me and tested the memory with Memtest for an hour, but no errors reported. I took the hard drive out, formatted it and ghosted a copy of my XP on it, to no avail.

I then plugged the dell hard drive into mine and set my PC to boot from it, which it did. So I unplugged it and reinserted into the Dell machine, still no joy! I took the PC6400 out of the Dell and tried it in mine. Mine read it no problem and worked fine with it in.

I have looked and the hard drive bay fan is working as is the front and back cooling fans on the dell machine.

At the rear of the dell are 4 diagnostic lights, and numbers 3 and 4 are lit. According to google this indicates possible memory failure!!

The machine attempts to reinstall windows but at the windows setup state it BSOD's and gives a blue screen stop message. googling this again indicates a memory failure.

Last night I ran memtest all night, it must have done several passes and when I got up at 7am it was just rebooting. I ran it again for 45 mins and it completed 100% passes / 100% tests over two complete passes. No memory errors showed.

When in BIOS it is fine and would probably run all day like that. As soon as I try to load XP onto the hard drive it gets to the screen when Windows is starting setup and does a BSOD.

My questions is what do I look for now? Do you have any ideas what it could be as I am flumoxxed as to what it could be. I thought it may be motherboard but am unsure and this would be a costly option to replace.