Sounds like a problem with the Passkey antitheft system. You'll have to get a shop manual to troubleshoot it.
http://free-auto-repair-advice.blogspot.com/2007/11/finding-repair-information-you-need-at.html
Corroded battery cables. Other than that you probably need to remove the starter and have it tested.
If a 94 Thunderbird starter will not turn over, the battery may be dead. The battery should be charged with jumper cables.
Is starter working?
Test the battery with a digital voltmeter. You should get a reading of 12.6 V if the battery is fully charged. If the battery is fully charged then you know the alternator is functioning properly and your problem is more than likely a defective starter.
Check the battery and see if it is charged or needs to be changed. Check the battery cables Check the starter condition
Starter solenoid? Battery not fully charged?
Check the starter.
If you are saying that you have reason to believe that the battery is charged, yet the starter won't crank the engine, it could be: starter, Neutral/park lockout switch, Bad electrical connection or Keyswitch.
because its gone bad the starter solenoid is engaging the gears, yet the motor fails to spin
Its a huge possibility your starter is out.
Yes, I do believe! But check battery and wires first. Any oil on starter? Good Battery amp's important
Is the new battery well charged? Is the starter bendix stuck? Is the starter ring stuck?