The sentry key immobilizer that reads the encoded information in the key fob is NOT part of the TIPM. The immobilizer sensor device is at the physical ignition key lock switch. So removing and reinstalling the TIPM would not generate a need to reprogram a sentry key to the vehicle.
Describe the noise that you are getting when holding the ignition key switch in the START position? Is a repeating clicking sound or just one click? Make sure the positive and negative battery cables are clean and shiny inside. Battery posts need to be clean and shiny. Even though they look clean there could be excessive resistance and preventing high current flow necessary to engage the starter solenoid
The TIPM is located between the air cleaner box tray and the brake master cylinder reservoir. Is it possible that working around the TIPM something bumped the 4 connectors at the PCM and caused a poor connection? Pay particular attention to connector C4 and make sure it is seated properly in its mating to the PCM. See image below.
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When you turn the ignition key switch to the START position is there a rectanguar box around the instrument cluster gear selector display indicating that the transmission is in PARK or NEUTRAL position?