The only other sign that there is anything wrong is when I turn the ignition on the heater light comes on, then it is replaced by an air bag symbol and then by the word "service", which after a few seconds goes out and the time/temperature appears.
Yes, there should be an OK when you turn on ignition. The fact that it reports error on both heat and airbag does indicate that there's a problem with the computer.
You should probably try to exercise the connectors.
If you open up the fuse box, the black sandwich box in the middle contains the computer. Lift it up carefully to expose the connectors on the back. Remove and re-insert each of the connectors one by one. If there is any sign of corrosion on the connectors, try to clean it off with a sharp knife.
Next step before replacing the computer would be to check all connections to the computer.
Perhaps also to remove the PCB from the sandwich box to check for signs of something burnt.
Good luck!
- Anders