I'm not familiar with FS2004 - but I have had similar problems in the past on other software.
Something to try (if you haven't already)...
1. Turn the graphics resolution down to minimum with all the effects and detail off. If it runs fine then start upping the res and if it still works start upping the effects/detail until it bombs out again.
Also, disable sound if possible, while you are doing the above. The final step would be to turn sound on again and test.
If the software runs fine in safe mode it suggests that some incompatibility is triggering the problem under certain circumstances. If possible, note down the settings the game uses when running in safe mode, and compare them to your normal settings.