Once its warmed up, TRY first gear, clutch in. Push.

If it feels almost the same as neutral, do iit. Point is, the difference in the LOAD you feel between rolling it in neutral and in gear is also what the starter and battery have to deal with. If you have a LESS than perfectly healthy battery, whether or not it starts COULD be determined right here.
First start of the day in cold weather? Think about it.