You'll only see the blue screen (BSOD) flash before it reboots if your PC has 'Automatically Restart' (reboots on error) still enabled.
If you want to see the BSOD in order to get a clue about the possible cause, you'll need to disable this setting.
Get into SAFE MODE (press F8 after the POST and choose SAFE MODE from the list).
Once Windows starts, press the WinKEY (the one with the Windows flag between left Ctrl & Alt) and tap the PAUSE/BREAK key to get System Properties box (or right-click MyComputer and choose Properties)
Choose the 'Advanced' TAB then see 'Startup and Recovery' (third item down) and press the 'Settings' button.
Take the tick out of 'Automatically Restart' then OK out of all that and reboot.
The next BSOD will remain on the screen and not cause the PC to reboot.
Now you can look for file name clues etc.
Dodgy drivers can cause a reboot because XP fails to load it (so it reboots to have another shot at it), so look for something your recognise.
If it looks like something like ATI or nvidia then it could be your display driver. Get back to SAFE MODE and uninstall it from control panel Add/remove programs.. Then reboot.
Hopefully, Windows will load it's default VGA drivers which hopefully will allow you to get online and download the latest drivers from the manufacturers support site.
Also check that your AV is updated and perhaps run a full scan as well.
Other common causes are dirty RAM
contacts, dodgy IDE
cables, bloated mainboard capacitors, ceased AGP or PCIe fans (overheating GPU
) and faulty PSU
's.. (the list can go on actually)