1996 Chrysler Sebring Hesitation on Initial Acceleration

We have a 1996 Chrysler Sebring Convertible, 2.5L. It was placed in Non-operation in 2006. A month ago, my father replaced the fuel pump in it, got it running, and drove it the 300-ish miles to me and my boyfriend as a gift. Three days later, as we were driving, we had no power on initial acceleration from a light. After releasing the gas, and accelerating lightly, we were able to slowly build speed. The car continued to have initial acceleration hesitation, but after hitting about 40 mph, it ran smoothly. Next few times we started it up, it sounded like there was some backfiring as well.
Since then, we replaced the EGR, it got a little better, but didn't fix it. We then replaced the IAT sensor, a little more better, but not completely fixed. So finally fed up, we took it to get a diagnostic done, they replaced the distributor cap and rotor, and the spark plugs, which we found out were the original 1996 Spark plugs. The mechanic said our fuel pressure and volume is all fine, so it couldn't be the fuel pump/filter. So we got the car back, and it started up much better, but after going down the road, we still have a bit of hesitation.
We're taking it back to the shop, but I'd like some direction. There's three sensors I'm thinking could still be the problem, but like I said, help is greatly appreciated.