Do you need to just resync your remote due to a battery replacement in the remote or car itself or do you need to program a new remote?
Replacing the BCM will require the remotes to be reprogammed. The problem is that you need a scan tool with the proper software to perform the programming. Here is the procedure for reprogramming if you have access to a tool. If not you should put a call into a local garage that does diagnostic work or the dealer. If it were just a battery change you could resync without programming.
KEYLESS ENTRY -2003 Saturn L200 Page 1 of 1
IMPORTANT:Up to 4 transmitters can be programmed. Do not operate or program the transmitters in the vicinity of other vehicles that are in the keyless entry program mode. This prevents the programming of the transmitters to the incorrect vehicle. The order in which the transmitters are programmed is important. The first transmitter programmed will be transmitter #1, and the second transmitter programmed will be transmitter #2. Use care to program the transmitters correctly.
Programming RKE Transmitters
IMPORTANT:All key fobs must be programmed each time any one fob is programmed. The scan tool must stay connected until all of the transmitters are programmed.
1.Install a scan tool. 2.Turn ON the ignition with the engine OFF. 3.Select Remote Function Actuation. 4.Select Special Functions. 5.Select Program Key Fobs. 6.Select the number of key fobs to be programmed. 7.Press and hold the LOCK and the UNLOCK buttons simultaneously on the first transmitter for approximately 15 seconds. The Power Locks should cycle to confirm programming of the first fob is complete. 8.If you are programming more than one transmitter, repeat the previous step to program up to four transmitters. 9.Remove the scan tool. 10.Exit the vehicle. Attempt to lock/unlock the doors to verify the programming. 11.Operate the transmitter functions in order to verify correct system operation.
I believe the TECH 2 tool used by the dealers can do this with a resync with the PCM.