1987 Volvo 240 DL Starts runs briefly then dies

Does it crank but not fire?
I would do the cheap things first - ohm out the plug wires, check the plugs, then the cap/rotor.

The fuel pump relay (the one behind the glove box) is known to go bad - I removed mine and reflowed the solder joints and mine never failed again - or you can replace that.

If your car is dead, check the negative cable to the battery that it's not corroded on either end.

Work on the wire jiggling thing first

Something not right there

It's possible that it's the fuel pump relay, bad computers or a host of other causes. The first thing I would do is to check fuses #'s 4 and 6. Rotate them in the holder as sometimes they get corrosion on them that hinders good contact.
You can put in a jumper wire from 4 to 6 and that should turn the pumps on and you can then start the car if the relay was the problem. Don't drive around like this as the pump will be on all of the time and it's not safe to have them in this state in case of an accident.

Sounds like you need a fuel pump. There is an access panel in the floor of the car to get to the pump.

Take off the fuse cover and note the location of the in-tank fuel pump & the main pump. If memory serves they are fuses 5 & 7. connect the fuses with a jumper to bypass the pump relay. The fuel pump will come on with the key off! Listen for the sound. No Sound No Pump.
If the pump works, try starting the engine with the jumper attached. If it starts you have a bad relay behind the glove box.

sounds silly but make sure there isn't a partial blockage in exaust system or a smashed pipe.

You have a bad ground connections somewhere.

the fuel injector's are self bleeding, most likely u have a fuel distributor problem.

Your talking about fuel pump relay,when was the last you had an tune up?wires,plugs,rotor,cap,fuel filter?