Can't use a used TSSM, they get "married" to a VIN. Sounds like the alarm is not currently armed, so you should be able to replace the faulty TSSM with a new TSSM or TSM.
Double check the fuse for the security system.
It is strange though that you are not getting any fault codes? :confused
If the TSSM was bad, you should get some sort of fault code.