Engine turns over but will not start?

My car had no problems beforehand, there were no check engine lights, strange noises, or smells. All of the electrical components were working as usual. After temperatures dropped it wouldn't start. It only makes the cranking noise as if it's about to start. The dashboard lights are on while it's trying to start. I changed the battery because the old one was badly corroded. The auto parts guy is recommending I change out the negative terminal then check if the starter, or alternator is having any issues. A friend of mine thinks it's an issue with the timing belt.