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The receiver is not your problem. Sounds like you have one bad fob and one bad tpms. You can try resoldering the connections in the fob. Search (using google) 'corvette forum legendary fix"
From what i have been told both key fobs and TPMS units work thru the same receiver . In a convertable it is mounted behind the drivers side rear radio speaker. U might want to pull it out and open it and make sure the antenna part is well attached. Mine was so loose it almost just fell off. So start by looking there and also put new batteries in the key fobs
So the batteries are dead. Get some replacements from Gene at GM Parts house. The bummer is you have to take the tires off the rims. Might just wait until next time you get new tires.
There is one receiver in the car and there are two types of transmitter devices , TPMS and key FOB's.
The transmitters encode a signal and data and transmit it. The Receiver decodes the signal (figures out which device sent the transmission) and passes the data to the BCM, PCM and IPC.
Other than both the TPMS and FOB's using the same receiver, there is no interaction between FOB's and TPMS.
You likely have two problems, bad batterys in the TPMS if they are original to the car and bad FOB's with broken solder joints on the circuit boards of the FOB's. The link that 65GGvert posted above addresses the solder joints in the FOB's. Here is a thread on replacing the batteries in the TPMS:
I'm having similar issues but also getting a code for "No Communication" with the receiver. How do I trouble shoot/test the receiver?I did check the wiring harness connection and it seems fine.