'77 F150

Sounds like the problem is not with the battery, but the charging system. Once the vehicle starts the engine should continue to run off the alternator. What is happening is you jump start the vehicle and it will run. The battery will continue to fire the plugs until it discharges to the point where it will no longer do so. Since the battery was dead when you purchased the vehicle check all the connections to and from the battery to the starter etc. You may have a loose connection or a dead short.

a charged battery not hooked up should read 12.5-13 volts with a multimeter,if when you start it and check the voltage with it running it should read about 14.5 volts on a working system. less than 12 your alternator isnt working. The voltage regulator could also be a problem its old enough and they are fairly cheap i would replace it, i would problably hook up a amp meter in between the battery and a cable with it off and start pulling fuses checking to see if anything is shorted when it is shut off.you might get lucky and find a bad circuit. My old 75 had a weak spring on the brakes that would light up the brakes and kill the battery off when you needed it. who looks at brake lights when you shut it off in the day time. good luck

to check your alt start the car,,,, then pull the postive cable off the batt, if the alt is good the motor will continue to run, if it stops the alt is bad,,,,, replace it.... an never get an alt checked at any auto zone stores,, there testing units only show if its puting out dosent show how much , an alt will restiure good on them even if its only puting out 9 volts