The remote works off a little circuit board that sends a radio signal to the car telling it to unlock the doors
The ignition has a small glass chip inbedded in the key which when the coil around the ignition is energised the chip becomes energised and sends a signal out that the car can then read, the chip and the circuit board are completely separate so just because one works doesn’t mean the other one will.
My instinct tells me there is likely a wiring fault or damage somewhere, you could spend days chasing it. If I were you I would get shot of the car while it is running, and get something else. The grandes are getting rusty now, and electrical faults tend to lead to more electrical faults.