When you turn the key it rolls over and starts for a second but then it quits.

Is this that Lincoln? No, you don't want to do that, in my opinion, some of those components you want to replace will have to be programmed, so you end up right back with the original problem.
This info for spare key programming.
Turn the ignition to run for 1 second with one of existing keys and then remove.
Within 5 seconds, insert a second existing key, turn to the run for 1 second and then remove.
Within 10 seconds, insert a new cut key, turn to the run position for 1 second.
All 3 keys should be able to start engine.
Sorry, that's all I have.

Is the security light flashing? did the car start run for a few seconds and then stop before getting to the point you are at now? if yes then you car has a security issue most likely the remote head key has failed and now by trying repeatedly you have compounded the problem and have a locked up ECU also.

Turn the key forward and try to start the car. If it does not start, look for a light on the dash that says SECURITY. If you see that light, that is the problem.

If it does not start, leave the key forward 2 clicks for 10 minutes, NO LESS. Roll the key back for 5 seconds and then try to start it.

You must turn the key forward 2 clicks until right before it would normally start. Leave like this for ten minutes. (No less) Roll the key back to regular position wait 5 seconds and repeat process. This must be done 3x in a row without starting in between. Whole process should take 30 minutes. After last ten minutes, roll back, count to five, then try to start your car. If this doesn't work, there is a way to bypass the system and never need that special transponder key again. This link explains. http://vatspasslockpasskeysecurityhelp.yolasite.com/

okay try this ,put key in ignition turn to on position for ten minutes ,roll window down so you dont lock keys in car before you do this. turn to on for ten minutes dont touch anything or turn anything on make sure all accesories are offthen turn key to off position for 10 seconds then try to start.
its important that you dont have radio or any accessory on during this process.

tw0seven0-fivefivesix-seventhreefiveseven

try turning key on and off 2or 3 times then see if it starts right up. if it is there is a check valve in the fuel pump. it cant be replaced. you would have to replace the whole sending unit. costs about $600.00

You have a bad Ignition Switch they are known to go out on the 90's audi's.

The part is pretty inexpensive but the labor maybe quite high.

When you start it make sure the key gets back to the proper position otherwise you will burn up your starter and cause another expensive problem.

This sounds like a security issue. Look into your manual to see about resetting it.

Be sure its all the way in park or try neutral.Its possible that security system does not recognize the key. Is security light flashing or on steady? Shut all doors and windows,trunk,hood, turn off all accessory's,roll down drivers window, turn key off and remove for at least 1 minute, insert key into ignition, try to start leaving key to run position for 20 minutes, turn key to off,wait 15 seconds, try to start again leaving key to run, wait 20 minutes, turn key off,wait 15 seconds, try to start, again leaving key to run, wait 20 minutes, turn key off, wait 15 seconds, try to start. This should relearn key code. It may relearn after 1 learn cycle and start if system is ok. Hope this helps and that the weather is dry and warm for this procedure! This is not always a fix, but works most of the time.

Remove the starter & inspect the contacts inside the starter solenoid housing. If they are burnt and/or worn, you will get this condition. Replace the contacts and the plunger, or replace the starter. I change contacts in my shop 3-4 times a week. Quite a common failure. The clicking noise is the plunger hitting one contact, but not the other, due to wear.