2001 Mercury Sable - Quit running while driving, will not turn over, fuel pump runs continuous, radio lights but does not play unless in reverse, lost theft light on dash but began working again, reverse lights don't light properly, no click at starter solinoid, all fuses ok, PCM does not communicate with test equiptment. Is PCM bad?

The first thing you must do is check for fuel delivery, you may have run out of gas even if the gage says there is fuel in it.

Are you getting fuel pressure? You have an inertia switch in the trunk and it might need reset(push the red button down). It shuts off the electric fuel pump in case you have an accident or get bumped hard.Sometimes they just actuate for no known reason.
Also crankshaft position sensor could be dead. Have you run the engine codes? don-ohio (:^)

Run the codes,change spark plugs,clean the MAF sensor and always make sure to replace a fuel filter every 30K miles. don-ohio

check and test fuel pump and relay

Hello
The Engine and Automatic Transmission (not applicable to manual transmissions) in this vehicles drive train are fully electronically controlled by a computer called the PCM and TCM (Power Train Control Module, Transmission Control Module). When a problem like this or other drive-ability related problems occurs the computer stores a record of the problem (there are of course some exceptions to this, like the fuel pump, engine coolant temperature sensor and MAF sensor for instance) in the form of a fault code in its memory, to read these fault codes you must have the systems memory scanned with a special tool. Once the fault code(s) are read you then must perform the appropriate diagnostic testing to find and resolve the problem(s) DO NOT REPLACE ANY PARTS UNTIL A TRAINED TECHNICAIN HAS DIAGNOSED THE PROBLEM TO AVOID SPENDING YOUR HARD EARNED MONEY ON PARTS THAT MAY NOT CORRECT THE PROBLEM. Also always check fuel pressure for correct spec for your make and engine type.

Very likely its the starter solenoid

Turn the key between the "off" and "run" position without engaging the starter. Can you hear the fuel pump turning on and off every time? The car SHOULD build proper fuel pressure, then shut the pump off until its been cranked or has sat for a while. If the pump never shuts off or is pumping every time its switched on and off, I'd say you've got a pressure issue or leak in the system. Testing fuel pressure isn't too difficult either. The tools can be "borrowed" from autozone or similar store if you don't own them already. Just buy them, do the job and return them clean and complete. I've never had a problem, even with "non-returnable once used" tools! : ) These stores can usually supply you with the proper specs if you need them. You may also want toi try testing the signal to the injectors themselves. Ahgain, tools avail at autozone and the likes. Good luck!

Sounds like you might have a stuck open EGR valve. Is the check engine light on. I would replace the fuel filter if it hasn't been replaced, also check the air filter.

u are going to have to replace the electric fuel pump, the pump uis located inside the gas tank.