1997 Chevy Blazer Fuel issue

Hello: Ok at one point the fuel sensing unit had come unplugged; seem to have gotten that taken care of. Now (about 10 months later) I am getting lack of fuel to allow the car to accelerate; stumbles; hesitates etc. Whole car seems to vibrate; I give it a little gas and get sputtering and it moves very jerky.
Seems worse going up hills. When I start it it seems like it does not want to start, like fuel is not getting to it like it should. And when I turn off the ignition there is a motorized noise for about 5-8 seconds coming from the rear end area.
If it is the fuel pump would'nt the car not start at all? Help this is really annoying! I am taking it to the shop tomarrow and would really like some information as to what you think they should maybe be looking at or for.
Thank you so much.