* Dead battery (even new ones): Check the voltage of the new batteries.
* Battery installation: Ensure the batteries are correctly installed, matching the polarity (+ and -) markings inside the remote.
* Remote malfunction: The remote itself might be faulty, even if the batteries are fine.
* Vehicle receiver issue: The receiver in your Blazer could be malfunctioning.
If replacing the batteries doesn't solve the problem, try locking and unlocking the doors manually with the key, then trying the remote again. If it still doesn't work, you may need to have the vehicle's keyless entry system checked by a mechanic or dealership.