sounds like there is a windows start up file or .exe missing. I presume it is the genuine factory restore for that PC so all files should be on the cd.
Could it be a hard drive fault where the file has been copied to a bad sector and can't be read during start up.
can you try the hard drive in the other pc again as a slave and run chkdsk/f or/r.
you can run check disk from my computer also. Open my computer, right click the drive and select properties. Move to the tools tab and there is an error checking option. Click check now and ensure both tick boxes are ticked and click start, this will tell you if there are any bad sectors.
Can you get into safe mode? If so, do this:
start/control panel/admin tools/event viewer/applications
do you see anything with a red ! sign?
click and read it.
Most likely it's a hardware problem, could be memory, hard drive, cd rom ect......
It's very unlikely that it's a software problem.
Before it reboots does it show the black screen with the windows logo?
When at the screen for safe mode is there an option to suspend automatic restarts (might only be with sp2), if there is can you select this and then see if it shows a blue screen of death with an error message. If the option to suspent restarts is not there you can install xp on another partition and disable restarts from the regedit.