Old Cobra alarm?
That looks like an old Cobra or Viper alarm remote. I would try replacing the remote's battery (see if the alarm responds after that.... if not....) , disconnect the car battery ground cable for about ten seconds then reattach the ground cable and immediately push one of the lock/unlock buttons on the remote. That should reprogram the remote to the alarm brain box. If that doesn't work the brain box is probably crapped out and you'll need to replace it with a new one. Most likely an updated version of the same company's alarm will plug right in. You can probably find the brain box behind the glove box (you have to remove the glovebox...). Pull it out and see if you can identify it. But try the new remote battery and reprogramming first and see if that fixes it. Good luck.