1999 Lincoln Town Car won't stay running

Check fuel pressure at the fuel rail. 20 years old fuel pump might be done.

If your fuel rail does not have fuel, your fuel pump may not be bad. It may be your security system. Lincoln made the transceiver wires too short. Continuously tilting your steering wheel up will pull apart one or more wires from the coupling underneath the dash. Trying starting your car with the steering wheel tilted completely down. If you are lucky, the wires may engage. If it starts, you can tilt the wheel back up and it will continue to run. But once you turn it off, you will have the same problem. Take your ignition out. Once it is out, your transceiver will slip out. Trace the wires under the dash (removing some under-the-dash plates will be required). Most likely, once you get to the coupler, will find one or more wires disconnected. I removed mine, took it in the house, and soldered the wire back into the coupler (pin-connector). But you are better off to replace "the wiring" with one from a salvage yard (wiring only - the transceiver is coded to the transponder in your key). The wiring has a connector on each side; one connects to the transceiver, the other end connects to the couple underneath the dash.