Starter not engaging
Take starter back to have it tested, if it tests good then check your cables to make sure you have a good connection. If all else fails, have someone look at the flywheel
Ditto on the flywheel
your starter might have some damaged gears. If the replacement starter does the same then I agree, check the flywheel.
Looking for a Used Tiburon in your area?
CarGurus has 501 nationwide Tiburon listings starting at $2,488.
Search Hyundai Tiburon Questions
Hyundai Tiburon Experts
Related Models For Sale
Used Cars For Sale