I have a small problem with my '97 400 GSi:
Sometimes when attempting to start the engine, the starter motor just spins (disengaged) and doesn't turn the engine over. I think it must be something to do with the solenoid that should engage it.
The solution is to operate the remote fob as if to open the doors and deactivate the alarm and immobiliser (even though I have just done this seconds earlier to get into the car). This is fine, but annoying, and occasionally takes a few attempts.
Is the starter solenoid linked in with the immobiliser? It's as if the immobiliser is deactivating, but the part of the system that should cause the starter to engage is not always operating.