I agree with pimpRunner that it's probably a wiring issue.
Here (attached) is the 2002 5VZ V6 engine control wiring diagram. There are some things that are different among various 4WD and / or auto models, but I don't understand why any of them should be throwing a P1135. None of them seem to have anything to do with the heated O2 heater circuit.
An ECM fault is listed as a possible cause for a P1135, but I have no idea what / where this fault may be.
NOTE: When you check your wiring, make a point to trace the wiring leading to your EFI Main Relay. A problem with the relay is listed from 2003 onward as a possible cause for heated O2 heater circuit codes. Beyond that - any fault with the EFI Main Relay would result in a no-start condition. This may be a big clue ...
NOTE: The diagnostic codes changed betweeen 2002 and 2003. P1135 is the old single code. As of 2003 it was changed to a set of 4 codes (B1S1 = P0031 & P0032) to conform to some OBDII standard. I don't see any changes in the relevant wiring between '02 and '03, so I'm fairly confident an EFI Relay fault would have been a problem in '02 as well.
Hope this helps ...