I would first check here:
http://www.necus.com/support/ for any driver downloads that you might need for your product. But these would only be able to be installed after reformatting the machine anyway.
If you are sure you have backed up all personal information needed on this laptop then go for it. If it fails you can still take it into a shop for a service.
Before you do this however, I would go into device manager and check what devices show up in there so you can compare this list when you re-install xp.
This machine sounds like a bit of a wreck to me (no offense), what will you use a laptop that has no screen for? It's hardly portable, but I understand if it was free!
Check you have the correct Certificate of Authenticity number (should be a label on the underside of the machine) and you should be fine re-installing the OS.