Stalling to not starting at all

(all happened right away after each other) First car's heat started pushing in bursts. Then the car started puttering. Then headlights flickering then the car would die out. it would start up right away, but then repeat the cylce, UNLESS i was accelerating .
the next day it wont even start.

:banghead:DOES ANY ONE KNOW WHAT'S WRONG:banghead:
:banghead: WITH MY:banghead:
:banghead:CAR?:banghead:

Need some more info.

Does the battery light come on during this?
Do the dash lights flicker along with the headlights?
How long does the car run after it dies before it dies again?
Will it continue to run as long as you accelerate?
Was your battery dead the next day when you tried to start your car?
Any other symptoms you can give during this would be helpful.

If i had to take a guess right now, i would guess something in the battery charging system. Probably an alternator.

Need some more info.

Does the battery light come on during this? no
Do the dash lights flicker along with the headlights? yes
How long does the car run after it dies before it dies again? keeps on running untill i let off gas then in about 30 sec's it'll die. the next day when started it would run in park only if i was accelerating then die again. but if it was in reverse or drive it would stay on but it sounded like it was gonna die but it didn't, unless i put it back in park
Will it continue to run as long as you accelerate?yes
Was your battery dead the next day when you tried to start your car?no

Any other symptoms you can give during this would be helpful.when i turn the key to the on position i can hear the fuel pump come on. now it'll turn over but not even start. about 3,000 miles ago got alternator checked and it was ok. but im due for another oil change.
If i had to take a guess right now, i would guess something in the battery charging system. Probably an alternator.

Sounds like you may have a fuel pump issue or perhaps a fuel filter. What year and engine is the car? The returnless fuel pumps are more susceptible to breaking. The sound of the fuel pump could just be because the battery is dead. The car may only have enough charge to prime the fuel pump thats it.

EDIT: I was thinking more about this. You could have a vacuum leak and the engine just sputters until it eventually dies. Either that, or for some reason, your running so rich the engine dies and you cant start the motor because its flooded.