Were you able to open it before and now you can't? If so what changed? Try going to the start menu (not the icon) and under Reaper there are several options. Try either Open Reaper (new project) or (reset configuration to factory defaults). Write back and give a bit more information and we will get you going.
Not really sure what's up, but I guess go back to basics. First make sure that you downloaded Reaper 32bit (since you are on XP) and re-install. You shouldn't need to un-install, but since it has never opened it might not be a bad idea.
Report back how you are doing.