Went to start my Durango, battery was dead.Charged battery (jumper cables).Battery was holding juice and turning, but no start up.Charged battery more.Attempted to start and used gas pedal.Truck started and killed.
Started again with gas pedal and upon startup, held the rpm to 1.5k.Slowly dropped rpm to 1k, then slowly dropped to idle.Killed.
Added 1 gallon of gas(Gas gauge said 1/8 tank, but we have had instances when will fill the gas tank, the floater(l think)locks up and says the tank is empty.Repeated gas induced ignition, slowly dropped rpm to idle the same way as before.My truck was then idling on its own.l let it run for a minute, and killed it.Lather, rinse, repeat.... another start-kill.l added one more gallon of gas.Lather, rinse, repeat.... l got it to run on its own.l turned off and restarted, and now it will not idle.l read on about the relay swap.l swapped relays.Started like a champ.To prove my relay theory, l switched the relays back to normal and attempted to start.It starts up with no problem.Lather, rinse repeat X 5 and no more problem.

My questions are

1)My battery was dead, but now holds voltage just fine.No lights were left on, so what caused the dead battery?
2)If the fuel pump is acting up, why is it intermittent, because 1 gallon of gas is not alot in this 22 gallon tank.
3) Was the relay sticking?The relay can not be permanently bad, l left the relay off and started the engine, it ran really rough and crappy, not the same symptom as before l swapped relays.
1999 Dodge Durango
Fuel injected

Jumpstart was sufficient, volt gauge on truck shows 14v and the turnover is smooth and not struggled.l have turned it over at least 10 times since the jump, no signs of the turnover slowing down, which usually happens with a battery that does not hold a charge.

how old is the vehicle?
is it a fuel injected engine?
change the fuel filter--running fuel from the tank bottom may have clogged it up
borrow a battery charger and do the battery the right way

a relay will sometimes stick in the closed position & cause this too happen it will drain a good battery down in no time,when u switched the relays u may have temporarily stopped the problem,if u have a 12 volt test light do a draw check on it to see if there is anything on with the key off that will be drawing power from the battery ,if its a relay this will show up & make the test light come on that is the only true way to find a power draw on one of those,i had one this morning that was doing like yours & it turned out to be a sticking relay that caused all the problems,sometimes though they wont act up all the time & r real hard to find,running a draw check may be the only way to find it,good luck.