car stops when driving still with new battery and alternator

[sunnyturner]

To Hello my 99 infiniti g20 is going through the blues.
It all starteed a couple of days ago when my boyfriend forgot to turn the headlights off while we went to get food, and suprise surprise car won't start. Luckily were right outside autozone.
So they give us a jump..boom! Car starts...now were good..
Well not really..bf puts car in reverse and bang the car stops immediately.
Hmm...so they charge the battery up for us....and were good until later that night when we are about to pull up to our house my bf puts the car in reverse and shortly after the car stops again..
Soooo some guys try to give me a jump and the cables started smoking....hmmmmmmm so I tell them to stop..
After this I notice that my all the meters on my dashboard don't work, the interior lights, radio, automatic power lock doesn't work..
We decide just to get a new battery and that's what we did.
We got the new battery yesterday and the car was driving fine until this morning.. we started the car, and it started slowly we pulled out of the messy snow after some struggle then not even after 100 feet the car stops and a stoplight...dang it..
So Ihave this truck push me up to the gas station to assuremyself its not the lack of gas that's a problem..nope its not.
So we have a guy give us a jump and hooray the car starts!
Thenn noooo its dies again.....
What could be possibly be wrong?