Ford - Mustang :: 1998 - Hard Start At Cold?

Simple question: Is it possible that battery problem/corrosion in battery cables would allow car to crank but not start on first try when cold? (Car normally starts on 2nd or 3rd try). I've read some places that if car cranks its not a battery problem but I'm not convinced.

Background:I have a 98 Ford Mustang (approx 140,000 miles) that occasionally has trouble starting. Car normally takes 2 to 3 tries to start first thing in the morning or if it has been sitting for a while. It always cranks but doesn't turn over. I had it in the auto repair shop, they said it had to do with IAC valve being stuck open. They recommended to replace throttle air by-pass valve. The repair was done and when I came to pick up the car I heard it take three tries to start before they brought it to me from the back. I asked about it, so the service advisor said he would go and talk to the tech, he said he talked to the tech and that there was a lot of carbon that he had cleaned out and maybe remaining carbon in the system caused problem, I got the idea that they seemed to think everything was fine if I had any problems I could bring it back. The car became even harder to start, now taking up to 8 tries. I brought it back and they said that the new IAC had to be adjusted to allow more air. I picked up the car, they said it was fine, but now it still takes 2 to 3 tries to start it first thing in the morning.

In the past, I have had trouble with battery and battery terminal corrosion, have had new terminal ends put on my battery a few times, last time was probably about 6 months ago. Terminal ends look very corroded again. I'm thinking about just asking them to replace the battery cables and see what happens.