Yes, you are right, there should be a splash screen with a choice of XP or Linux. Grub is the boot loader. It should detect the two operating systems and show them. It looks like grub is not working.
The first thing I would try is rebooting the computer with the Fedora CD in it. You should get a list of options, one of which is "Repair Installation", or something like that. Select that one, and go through the screens, reading everything. Somewhere in there it should give you some options for setting up grub again. You should not have to go through a whole reinstall.
Try that and tell us what happens. Good luck.