I don't think you have done any damages.
The same thing happened to my car last week.
All winter long, at temp. down to -40deg. the car always started like it was 75deg., no ever turning 1/4 of a turn on the starter before it fired.
Last week, on a nice balmy morning (32Fdeg), it barely started, being very slow to turn on the starter.
The next day, even warmer weather (35degF), all I had was a faint "click".
A new battery solved the problem.
JackD