If it was a transponder fault in the key the PATS light would flash constantly indicating a bad Key or receiver ring.

I don't know if a snap on would read the PATS module. It is a timed 10 minute access into them anyway so you cant find out straight away. The have a flash code system using the Red LED on the dash anyway so if it was at fault you can soon find the fault if it is the system.

I take it you have checked your fuses??