grand am won't start

I left a post about 6 weeksago explaing i have a 4cyl 1990 grand am that I had been using as a secondary car. I now want to give it to my niece. Here's the problem, I parked the car at the end of last summer and like a dummy I didn't bother to start it at all over the winter. I live in NW PA. and the winters are very cold. Six weeks ago I tried to start it with no luck. It would not jump start either. So I just bought a new battery. The battery was definetly (part) of the problem, but not all. It still won't start. When trying to start, it sounds like a car that's out of gas. It has about a third of a tank left over from last summer. So I put in 5 gal. of high grade gas and two bottles of dry-gas. Still no start. finally I tried the old trick of pouring about 1/4 cup of gas into the carburetor. When I do this, it actually starts, but it cuts off after 4-5 seconds. I've done this about 10 times and the longest was about 9-10 seconds. Also, once it starts that first time, that's it. Any attempt after that it goes back to sounding like a car out of gas. What you have to do then is add more gas to the carburetor and it will again start up for a few seconds. The process then just repeats itself. I'm no mechanic and I'm sure I could be wrong, but it seems as if that little gas I put in carburetor is just enough to fire and start the engine, but then for some reason it is not getting any more gas to keep it running. I feel sure it's a fuel problem, but not positive. My question is what suggestions or tricks of the trade i might try to get to the source of the fuel problem? Is there a process of elimination I should follow and what do I look for. Like i said I'm no mechanic, but I know my way around an engine so-so and no fear of getting in there and doing the work! Any help or suggestions would be very, very much appreciated. THANKS

You should turn the key to the run position and listen for a whirring noise at the tank, if you don't hear it, try moderately hitting the bottom of the tank while someone cranks it over. If it attempts to start or starts odds are the fuel pump. Check your wiring and fuses also

You said that this vehicle uses a carburetor and not a Fuel Injection?
If this is a carburetor, then open up the carburetor cover (air horn) and see if there is any fuel in the fuel bowl. If it is empty then pour some gas and fill it up and put back the carburetor cover (air horn) and try to start the vehicle again.

If the vehicle starts and dies later on (a couple of minutes), open the carburetor cover again and check to see if the fuel bowl is empty. If it is empty again then you know that it is not getting fuel.

Check the fuel filter near the carburetor or replace the fuel filter. The fuel pump usually has a relay/fuse. Check the relay/fuse and replace them if they are defective. You can actually bypass the fuel pump relay and directly feed the fuel pump with a 12 volt source and see if the pump starts working again.

I agree with slade , also if it sat so long could be the float in the carb is holding to much moisture and is simple and cheap to replace.

this car cant have a carb, it is most likely tbi,which looks very much like a carb. Probably a 2.5 4 tech engine, i have one of these in a cutlass, if the fuel pump runs then it is most likely the crank sensor which tells the injector when to inject

If this vehicle is not a carburetor but a TBI (Throttle Body Injector), you have to use fuel pressure gauge. Since TBI does not have a schrader valve where you can just screw in the Fuel Pressure Gauge, you have to have a T-connector to connect the Fuel Pressure Gauge to the fuel inlet going to the TBI.

If you don't have a Fue Pressure Gauge, your other option would be to try to locate the fuel pump relay/fuse in the engine bay. There should be a section in the fuel pump relay/fuse that allows you to by-pass the fuel pump relay and directly connect it to the 12 volt battery source. You should hear the fuel pump working. If the fuel pump starts working, try to crank the engine while you are still by-passing the fuel pump relay and see if the engine turns over and stays running fine.

Sometimes the fuel pump, radiator cooling fans are using the same identical type relays. Try to locate your radiator cooling fan relay and swap it with the fuel pump and see if that works. If your radiator uses two fans then use the secondary cooling fan relay. Only swap the relay for testing purposes and if the fuel pump relay is indeed bad then purchase another one and put back the good relay back to the radiator cooling fan.

Another possibility would be a clogged fuel filter and lastly you may have a failing fuel pump.