So, refresh the brain.....
You have two keys......one for the door lock (physical) and one for the ignition...?
You are currently opening the car with the door key, then starting with the ignition key.....yes?
Previously you were able to unlock/lock using the ignition key remotely....? Now you can't...?
The alarm will go off because as far as the car is concerned it hasn't recieved a signal from an 'authorised' source...i.e. the remote signal from a synced key....and will set the alarm off until it recognises the correct key signal - which is done when you place the ignition key into the barrel and the coil picks up the transponder in the key......the alrm switches off and the engine re-mobilises.....this system is working exactly as it should.
Have you tried.....
Put the Door Key in the door lock, turn to lock and press the ignition key unlock button, now turn the key to unlock and press the ignition key unlock button.....get in and start the engine with the ignition key.....
Turn off the engine, get out, close the door and see if you can lock/unlock using the ignition key remotely now.....
This is because the car may need to see a physical key movement coupled to a remote signal......
It may work, it may not, but worth a shot.....