Fuel Pump Problem??? 1997 neon

My 97 neon is having a hard time starting up, it basically hesitates for the first turn of the key, then starts on the second time. I just recently got all the spark plugs and battery changed so those aren't the problem. I also got the fuel injection cleaned so i don't think that thats the problem either. A local mechanic took a look at it and said that it is most likely the fuel pump, but to replace that is a 500 dollar deal and i'm not looking to spend that much. Do any of you know another thing that it might be? Or something to help, that doesn't involve paying 500 dollars? any ideas are good.

Put a fuel pressure gauge on the port on the fuel rail (can probably borrow one from Advance or Auto Zone)and with engine running, check the pressure, should be about 49 psi (this will tell you if the fuel pump is putting out enough pressure). You can install a pump (if needed), it goes in the side of the fuel tank and a lock ring holds it in. Haynes manual is really helpful here and Auto Zone website has pictures and text on this operation. (Pump is about $185.00).

Let me back up. First, when you say it hesitates on first turn of the key, do you mean it does not really turn over or the engine fires and dies. If she is hesitating on the start I would check both the battery posts (clean them) and the starter connections at the starer for cleanliness (no crud). Do you hear the fuel pump buzz when you go to start the car? Also take a fuel pressure check at the rail with engine off but key on, see what pressure is being sent to the rail.

When i say hesitates, i mean that it doesnt turn over right away, eventually it will but it'll take a couple seconds. I don't really think it has anything to do with the battery because the sound isn't that 'clicking' sound that it would make. I'll try to test the pressure of the fuel pump.

Before you go too far, put a volt meter on the battery and take a reading (with engine off), you should see about 12.0 VDC, then have some one crank her over while holding volt meter leads on the battery and see what she reads, should not drop below about 11.0 VDC (if battery is really flat you would get the click,click). Also while the engine is running do the same voltage check as before and this will test the alternator out put (need to see about 14.0 VDC).

idk if this makes a difference at all, but i did just get a tune up and got it inspected and all that so aren't these things, like battery issues, things that they would have seen when they did it?

Todays tune ups generally consist of replacing the spark plugs, PCV valve, checking the belts. I doubt that anyone checked the battery or alternator.

not sure about the alternator but i got a new battery in addition to the tune up.

Our 97 Neon would crank over v-e-r-y slowly the first time. The second time it would spin okay, or if I just held the key in the start position longer. I removed the starter and opened it up; thinking its brushes/commutator were coated with that gummy mixture of grease and graphite shaving. They were, but the brushes were worn down to the thickness of a fingernail! A rebuilt starter solved my problem. The car had 141,000 miles on it.

k well after testing the pressure and stuff, i found out that my problem was that for some reason, when i turn the car off the fuel pressure goes back down to zero, instead of staying up like it should be (it should right?) So my best guess is theres something in the fuel pump not working correctly, and i think i'm gonna just deal with it instead of paying 500 to get a new one installed.

Yes, the fuel pressure should stay up. Ours stays up for at least a weekend - and it never sits longer than that, so it may stay up much longer, I dont know.
When you first turn on the ignition, the fuel pump should run for almost 2 seconds. In a quiet location you can hear the soft hum. This would normally bring the fuel pressure up to the proper amount for starting if it wasnt still pressurized from the previous day. Assuming your problem is back at the fuel tank: If your fuel system will hold pressure for even a few seconds, you can turn the ignition on once to bring the pressure up, and do it again a couple of seconds later - and hopefully the engine will start quickly. (Thus not wearing out the starter.)
The fuel pump could have lost its 'anti-backflow' feature, or the pressure regulator could have a 'leakdown' problem'. On my 97 Neon, both the pressure regulator and the pump are located on/in the fuel tank, on a module that comes out after the (emptied) fuel tank is lowered. I think that if the problem is the fuel pressure regulator (which is also the fuel filter) leaking-down, it may lower your fuel pressure generally. If it lowers it enough, the computer wont be able to compensate by pulsing the injectors longer, and the engine could be running 'lean' at higher rpm and large throttle openings.
Loss of fuel pressure can also happen if one or more injectors are leaking - but I think this is very rare on Neons. It sometimes happens on the older VW Jettas if they have high mileage (like 200k miles).