since your internet is working fine, besides uninstaling IE and reinstalling it again, try scanning the computer for any malicious spyware and viruses.
also if you have your own copy of windows xp, try putting in the cd in the cdrom while on windows. then go click on start -> run -> type in "sfc /scannow" without the "". after this process is complete reboot the computer again. then when you get to windows see if you can click on the links while you read your email, good luck.