EEVEE

Hello my 99 cherokee has been sitting for a while so i put gas in it to move it its at 3/4 of a tank now (been filling up when i have left over gas). and has started fine with stalling before but i was suspecting it was just low on gas with moisture inside it so i heeded the advice to fill it up to a decent amount. so when i went to start it after putting a deep charge on it like 15 hour charge on 2 amps it seemed decently charged it turned over on its own but it just wouldnt start it kept cranking over with it on the verge of starting but wouldnt start and then the battery died. so i got the battery booster and put that on and it cranked for a long time until it sputtered to life i mean i was holding the starter to start it (i know thats bad to do for a certain amount of time) so it was idling so i could warm it up and charge the battery with it idling then i went to roll the windows down and then nothing so i took the door panel off and it was unplugged (it was loose and slipped off) and then i plugged it back up and then all the controls worked on the door. i was putting the door back together then it started to sputter badly and i was hitting the gas and it wouldnt rev at all it was just constant sputtering and then died so i tried to crank it over again and wouldnt start at all just cranking over till it died which was like 10 turn overs. so then i got the booster again with the addition of hooking the battery charger on 10 amps the i went to crank it over and fired right up like nothing was ever wrong. so i took the battery charger and booster off because i was expecting my uncle to come soon so i tried to move it around i went around the back yard a bit with it moving on idle not hitting the gas so first test passed the i hit the gas a bit steadily and went fine the floored it and burned out on the grass so it was fine i thought so i was curious i took it on the road across my driveway which is like a 7 foot length lol so i floored it and when i did it burned rubber (i was happy it still could do that lol) then i noticed when it got done skidding out it just lost power and was at a constant rpm till i hit the driveway and then hit the brakes. so i was like thats weird so i did it again with the same results i did this 4 times it wouldnt go past 2500 rpm so i was done with that i was talking with my dad and said the battery sounds bad is that true a bad battery can cause that or a bad fuel pump? i couldnt go on bigger roads to test this because of no plates thus is why i was waiting for the transporter plates from my uncle i was planning to take it to my dads to store in the garage to the suns not beating on it and fix it up a bit.but he couldnt make it but back to the question is it the battery that can cause that or bad fuel punp or a bad alternator?