Here's what you should try:
* Check the hood latch: Sometimes a slightly ajar hood can trigger the alarm. Make sure it's securely closed.
* Check the other doors: Ensure all other doors and the tailgate are properly closed and latched.
* Find your key fob (if applicable): Even with the broken driver's side lock, if you have a functioning key fob for your vehicle, try using that to disarm the alarm.
* Use a spare key: If you have a spare key (even if it's a valet key that doesn't open the doors), try using it in the ignition. Sometimes this can override the alarm system.
* Manual override (if equipped): Some older vehicles have a manual alarm override switch hidden somewhere under the dash. Consult your owner's manual. This is less common in 1993 models.
If none of these work:
You'll likely need professional assistance. Calling a locksmith specializing in automotive locks is your best bet. They have tools and techniques to disarm the alarm system and deal with the broken lock without further damage. Towing the vehicle might also be necessary depending on the situation. Trying to force anything could potentially cause further damage or injury.