This looks like a corrupted save. You're going to have to use a backup.
Coincidentally, a new patch is up now that fixes both of these issues. You may have to get the Ariados again, but the main teleporters do work after stepping on the ones in the gym.
This patch also (should) fix that cell issue people have been experiencing. (If you got stuck by a turret, reload a backup save. It won't lock you up again.)
Crawli's gym also got some tweaks, so it should be less buggy there as well.