Sounds like your ignition switch is bad. You can replace it but requires taking the whole inflation key Assembly out to install a new switch in it. To test this, open hood and pull the plug off the starter (in pic, I have the plug pulled off from where the yellow connector with brow wire is). There are metal locking clips that act as handles. You squeeze then together as you are removing the plug. Now, to test my theory ( if you have standard transmission, make sure parking brake is set and it's in neutral), touch a wire from that terminal to ground (any bare metal on the car). If it cranks, ignition switch is the problem. Remember the yellow connector with the brown wire o mentioned? Well, that's my easy fix. I ran a wire from the terminal on the starter, through the firewall (just found a grommet with other wires already going through the firewall and poked it through) and then over where you probably have a blank switch cover (covers the hole where a switch could be for an accessory your car didn't come with). I'd tell you to go to radio shack, but it... If you have a local electrical supply store or maybe even computer store like microcenter, get a momentary single pole single throw switch (mine is just a small black push button) that is around 3/8" in dinner Max. With the switch cover off your dash, drill a hole the size to match the threads of the switch. Solder the wire from the starter that you ran earlier, to one terminal of the switch. Find a good screw near the hole that the blanking cover came from and that is screwed into metal to attach a wire to (you can just strip the end of another piece of wire like the first one but only long enough to go from there screw to the new switch. Solder the other end of the wire to the other terminal on the new switch. You might have someone help you before you solder it to make sure everything is going to work. All that's left is to attach the new switch to the switch cover that you drilled the hole in and snap it back into place.
the great thing about this is, even though you still have to have the key in and turned on, it's now a push button start just like the newer cars. Also, a little bit of a theft deterrent.