my guess is that the bendix (starter engagement solenoid that pushes starter
"into" the starter gear) has gone bad or needs cleening&light lubricating.
the worse scenario is that the starter gear is missing some cogs... , and it
accidentally stopped in the wrong place.
Try pushing the car a bit, while it is in a gear. If after that it still
doesn't engage, dismantle the starter and it's solenoid (bendix), and check
It sometimes happens, in cold weather, that a few attempts are needed before
the bendix manages to do it's job...