Cold hard start and fast idle

I have a 1993 Buick Park Avenue 3.8 V6 with 131,000 miles. I had a battery and starter 3,000 miles before that. I took my car for an oil change at a dealers and they said I had an oil leak. My car was running perfect before this. They put an intake manifold gasket and a coolant flush totalling $700. When I got the car back, the cold start up was rough and the car would idle real high, then drop down to a fast idle. Once the car warmed up, it would start fine and idle at 750 rpms. I took it back and they said a fuel injector was sticking and they cleaned the fuel injector system. The car still cold starts bad and the idle is higher but drops down off the 1500 slower. The start is cranking hard and you think it started and isn't. It does not throw a light but it is not acting like I am used to--it was always an easy starter and ran good--even in really cold weather. Also, when you let off the gas while driving, it does not sloww down right away, it sort of hangs at the same speed for awhile. I use hand controls so the way my car acts is really important because it is the only car I can drive. The dealer says its fine but it isn't. They said the fuel injector threw a couple of false readings on sensors. It feels like something is still sticking or something. I have it at another mechanics to check the cold start--will it show a code even if no red light came on.