1. Make sure there are no MOD related files installed. (Even though you reinstalled, it's possible the files were left there. Many uninstallers will not delete files that weren't made by the installer.)
2. Try upgrading your video card drivers, sound card drivers, etc.
3. Go through the launcher's Setup and redo the video card/sound card stuff.
4. There are some errors for which FS2 will not display an error message. They're called GPFs (General Program Faults) also known as the "Illegal Operation" messages that programs tend to pop up. Because FS2 runs fullscreen, you wouldn't be able to see those messages. Instead, FS2 will crash to the desktop and the error message info gets appended to a file called errorlog.txt which is stored in the FS2 main folder and should contain a record of all the GPFs since the last time you deleted the file. (Don't know if the uninstaller will delete it or not.) The error info may be in there even if FS2 crashed before it started the intro movie. Each entry notes the date and time the error occured along with lots and lots of other info.
5. Make sure the WinXP compatability settings for fs2.exe are set right. (Remember, the actual program is not freespace2.exe, it's fs2.exe. Freespace2.exe is the launcher.)
6. If all else fails, uninstall FS2, manually check to make sure the FS2 main folder is gone, if you know how to use Regedit you can see if the registry entries are gone, and then reinstall.