Door locks and keyless entry doesn't work

When I purchased this car (used), I was not told that there was something wrong with the keyless unit. However, I was given 1 ignition key that only opens the drivers door and back hatch door and 1 key fob that doesn't work anything. I have changed batteries, tried to reset with the door button and nothing works. I finally took the car in to the SUZUKI dealership and had a diagnostic testing done. I was told that the computer needs to be replaced at a cost of $750.00. My question is this. Why does the car operate at all if the computer needs replacing? I drive it every day, however, I would feel more secure if the alarm system could be armed via the door locks.