2001 Corolla, hesitates on acceleration, hard to start, CE light has been on for over a yr but it has 138,000 miles, a friend says the trouble code says "running lean". I changed the fuel pump about one year ago because of the same problem which was not nearly as bad at that time. New fuel pump did not really make it any better and it gradually got worse. Fuel pressure regulator was not replaced when pump was changed. In the past two months, I have had it on computers at 3 different shops (two were free, one was about $100). All 3 said it was missing on cylinders one and four and running a little lean. The first one said I needed a new coil pack. I got one $120 and tried it on each cylinder. It was no better. Second shop said it was missing and “maybe running lean”. Third shop said the same & they changed the plugs yesterday. It is now much harder to start but supposedly not missing on cyl one & four now. They asked me to bring it back next week when they have time to put it on the rack to listen to fuel pump. They think my car's computer may not turn on the fuel pump consistently, but I always hear it when I turn on the key and for a few seconds & also after I turn off the motor. Third shop had me get catalytic converter checked at a specialty shop. It is working fine. When car was about one yr old, it began to hesitate or stumble on acceleration about once every month or two but only when I first backed out of driveway in the morning and shifted from reverse to first gear. I could overcome it if I patted the accelerator up & down a little. When it hesitates, it will speed up a little each time I let off the gas when I pat it up and down.

Optional Information:
2001 Toyota Corolla 1.8 liter

Already Tried:
I changed fuel pump about a year ago (when this problem was not quite as obvious). Was told the diagnostic code said it was a bad coil pack. I bought one new coil pack and tried it on each of the four cylinders. There was no improvement. The old coil packs seemed to have just as much spark as the new one. Catalytic converter was tested and is fine. When it is hot, I sometimes have to add a tiny bit of gas or starter fluid to air intake to get it to start. Otherwise I may have to try the starter several times for much longer intervals than I would like to. I don't like to hold the key to keep starter going for over 30-40 seconds at a time.