1989 Buick Park Avenue trouble cranking

I have a 1989 Buick Park Avenue. It's a good little car, BUT! For the last few weeks, it has been hard to get started the first time each day. After it's started, there's no problem cranking it up for the rest of the day, so it's only when it's cold. My mechanic is a very honest man (believe me! I know this for a 110% fact!) He put a new fuel filter on it. The old one had rusty water all in it. He thought that might take care of the problem, but nope! So the next day I called and he said bring her in. He's put a new pressure switch on the car this time. Not fixed. It's hard to know if the car is fixed right away, because it's only when it's cold that it has trouble being started. I have to turn the key usually several times before it will start. Also, I sometimes press the accelerator. I have to call my mechanic tomorrow. Does anyone have ANY suggestions or ideas as to what's up with my car? ?
janet