1989 Bronco w/ 302 Starting trouble

I have an 89 Full size Bronco with a fuel injected 302 and automatic transmission. The only time it runs while starting is in the (key turned all the way) start position. It fires up and I let go of the key and it stops running. It doesn't die or sputter, it is like I turned off the igniton. (Tac drops like a rock, and doesn't make any labored sounds, just like I turned off the ignition.) How ever, if you crank it so it fires you can disconect the cable that runs from the ignition to the starting solonoid and it will run. However if you touch that cable back to the solonoid, it will just kill the engine. Also when you put it in any gear it dies (while the cable is removed). Also if I let it warm up and and put it in gear a few times (letting it die) it will start running with the cable connected. I have replaced the ignition switch (mounted on console under dash), and it still has the same problem. As far as I know that wire only tells the solonoid to open and give power to the starter. Has anyone ever had this trouble, or know how to fix it?

Could it be the Lock-cylinder itself? There are connectors (obviously) that tell the ig switch which position the key is in...I don't know how much a new one would cost but it may be worth a shot. I remember taking mine apart for some reason (Lost to history) and it must have fixed whatever I having problems with.

Well with a little googeling, and my trusty old Chilton manual...it turned out to be my TFI. Pretty simple fix for such an irritating problem. I had one mechanic tell me it was my main fuel pump, another tell me it was my ignition switch... and it turned out to be something I could diagnose and fix (unbolt and plug new one in) pretty easy.