Recently my car refused to start. It wasn't a dead battery because it didn't make a clicking sound when I turned the key. It went thub thub thub but wouldn't kick in and start. The next day when I tried, it started like a breeze, and continued to do so for several days. I took it to a repair shop and they couldnt figure it out. They said the starter was good, and the battery, and they tried starting it 20 something times and it started right up. Then a couple of days later it happened again, late at night. It was cold. I tried starting it and got the thub thub engine-turning-over sound. I waited 10 min and tried again. Same thing. I waited another 10 minutes and tried again. This time it thubbed and sputtered and tried to catch, so I pressed hard on the gas and it started, but there was a screeching sound like maybe a belt(?) It screeched exactly when I pressed the gas. This has happened several times since then as well. It doesn't happen when I press the gas at other times, such as on the road, but only when starting, and only when its a hesitant start. The other situation that happens sometimes is a nice clean start, no hesitating/sputtering and no screeching. It seems that maybe the problem happens more when its cold out although I haven't experienced it enough to be totally sure about that.
P.S. I know very little about cars, like I guess the majority of women. I would love to see a diagram of my engine with parts labled so I can know what I'm looking besides just the oil stick when I open the hood. Does anyone know where I can get something like that?
I forgot to mention, my check engine light is on, and has been for some time now. I use premium fuel all the time so I know it can't be that. I have no idea if its related to the starting problem.
Thanks for your advice.