Transistor letting 12Volts through collector->emmiter withouit being damaged
You've probably mixed up emitter and collector. 

If the transistor is connected backward, it will sort-of work (with very low hfe), but Vce(br) will be about 8-9VDC, so you'll get the LED lighting without an input. 

Breaking down the B-E junction is not good for the transistor and can permanently reduce forward gain, so if this turns out to be true you may as well splurge and use a new 2-cent transistor.