Please Help

Saturn SL1 or Sl2, not sure. In ohio, crazy cold here. My battery died, which I fine, I understand. Bought new battery and car started rite up. Wife took it to work the next night, came home in the morning. I got up for work, went out to the car and engine will not turn over at all and no clicking. But heater and other electrical aspects work. My wife had the car towed to the mechanic. The mechanic goes out into the parking lot to drive it into one of the bays and the car starts rite up, and he did this a couple times during the day. I stopped by after work, took my car home. Work up the next morning for work. Started my car, drove to work. Went to leave home for the day and the same thing happened again. So my car is at work and I don't know what to do. I'm not sure if it has anything to do with the cold and or the started getting jostled around during tow and that loosened it back up and then froze again while at work in the wide open? I am by far from a mechanic, any advice would be greatly appreciated! Thanks in advance!!

Is this an automatic? If it is, the next time it won't start, try moving the shifter from park to neutral and trying it. If it starts, your neutral safety switch is worn out. You may have to wiggle the shifter around while keeping the key turned on to see if it will start in neutral.

Try removing and reattaching the battery cables to the terminals. These cars are very sensitive to loose battery cables. As previously mentioned, the park/neutral safety switch (automatic transmission) or clutch pedal switch (manual transmission) could be bad too.