SL1 will not start

About a month ago I had my SL1 serviced, everything fine or fixed.
In the past week we had some snow and low temps, the SL1 would not start. This happens every time snow and low temps come about.
Now though it has gotten warmer, still the car will not start.
When I turn the key to the Run position, the electric displays at first work normally but then a few stay on.
When I turn the key to the Start position, I get a clicking noise but no turnover sound from the engine, just the constant clicking.
I have no idea what is happening despite reading the manual and a Haynes Repair Manual.
What is wrong?
Thanks.

How old is your battery? Put a voltmeter on the battery when someone tries to start it. Sounds like it's dead or bad cell. Please don't respond with "all the lights are fine". Voltmeter.

How old is your battery? Put a voltmeter on the battery when someone tries to start it. Sounds like it's dead or bad cell. Please don't respond with "all the lights are fine". Voltmeter.

Actually the battery just got replaced last service in the past 1-2 months.

Actually the battery just got replaced last service in the past 1-2 months.

Like I said. Voltmeter.