Q: Car will not start and interior accessories are disabled. 1998 Saturn LS

1998 Saturn LSMy car will not start and I am considering that it is caused by the security system shutting down the ignition system in my car. The battery is functioning just fine. What happened is that I turned the key to start the car and when I do, it does not produce any click. Also disabled are some of the interior accessory powered parts like the radio, door locks, clock, etc. The lights do work, as well as the horn and wipers. I jump-started the car but it didn’t help. I could bypass this problem sometimes by disconnecting the battery, then waiting a while, and then reconnecting it. Eventually this will work, but I have had to wait for days for it to work. It is actually the only way it will work! If the clock and the radio come on, then I know the car will start and then the door locks also work. This problem is intermittent but I can’t really drive anywhere because I do not know when it will occur. As mentioned earlier, I am thinking that the problem is associated with the security interlock because I had this exact same problem when the remote keyless entry system disabled the ignition. More than one year ago, I had stopped using the remote keyless system and the problem is now back. I have been to two different auto repair shops and neither of them can fix this. In your experience what will repair this problem?