Hmm. Try this:
1) Check your harddrive for viruses.
2) Run scandisk to correct any errors.
3) Restart your computer to refresh the system resources.
Now, some questions. What version of Windows are you running? If it's Windows 2000, perhaps that might explain it. Did you buy this CD from a retail store (maybe your CD is defective)?
Did you do a full install of JK?
Did you install JK into a clean directory, is it in the same directory as another game (like the JK demo or MOTS)? (if it is, then that might be your problem).
You might also try doing a windows update and installing any critical updates, and getting your latest drivers for your video card, getting DirectX 7.0a, and installing the JK 1.01 update, but it probably won't fix anything.
If you haven't already, you could try running the system identification utility that's on the JK CD. You know, the one that checks to see if JK can run on your computer? It will probably say you can, since your specs seem to check out, but you never know, it might point out a problem you haven't thought of.