These older alarm systems are a pain in the butt. You might try unlocking the trunk and see if that de-activates the system so that you can start the car. Then I'd get myself over to a competent car alarm shop and rip the whole thing out and throw it away. Your system works on a series of sensors in the doors, the locks, the trunk the engine hood, etc., any one of which could be failing to send a signal to your alarm module. I'm not sure why your remote fob isn't working but this suggests at least a faulty transmitter in the door. If you have to have it towed to the alarm shop, well that's what you have to do. Most of the alarm apparatus is under the hood, on the right fender, but disconnecting that probably won't re-activate the ignition without further work from the alarm people.
The dealer has a computer CONSULT system that can diagnosis all this, but that could be expensive.