If gasoline is allowed to sit for any great length of time, it will slowly change composition into something resembling pitch. When this happens in a DeLorean, it not only ruins the pump and the ancillary parts in the tank, but the fuel injection apparatus in the engine bay.
When dealing with a car that has sat, unused, for many months or longer, start at the tank. Take the pump and boot out of the tank and pull the baffle and the stuff connected to it out through the large hole where the pump goes in. There is no need to drop the tank. That hole is the only access to the inside of the tank, you may as well leave it in the car. Access it by removing the spare from the luggage compartment, the access panel under the spare is there for this purpose.
Clean the inside with a strong organic solvent. Lacquer thinner or the equivalent is best, although fresh gasoline will do. In any case, be thorough. Siphon the old gas out as completely as you can then wipe the rest out. Use the solvent to dissolve and wash away any accumulation of sticky residue. Be rigorous about this. Don't leave any. Just a small amount will re-contaminate the new gas you put in and will likely ruin your new pump. Replace the pump and associated bits with ones from DMC's Fuel Pump/Sender Module, it replaces all the items that are prone to deterioration and is a modern replacement for the original, trouble-prone internal tank components.
Now work your way toward the engine. Replace or drain the fuel accumulator. There's bad gas there, too. Install the new filter from the kit. At this point you may try to run the engine. If it runs at all, it will probably be quite rough, due to the effect of the sticky gas that has been left in the small clearances of the mechanical fuel injection. Start by replacing the injectors and seals, then move to the fuel distributor and the control pressure regulator.
Two things that you can do before replacing those last two are to free the plunger in the fuel distributor if it is stuck by the contamination and clean the screen below the larger fuel connector on the control pressure regulator. These procedures may not fix all the problems caused by fuel contamination, but can possibly bring original parts back to life. They're worth a try.
Revised DAS 6/22/2016 [added access link]