2001 Pontiac Grand Am car won't start but lights come on?

2001 Pontiac Grand Am Automatic

my car has a problem where when it's cold in the car, it won't start. I turn the key over all the way to the right and all I hear is "tick" and that's it. Some lights some on and go back off trying to start it but like I said, every time I turn key over to right all the way, I just hear "tick". It's just one tick I hear. I don't know what to think.
the shop replaced the bad battery that was corroded and such and cleaned the cables and everything for the new battery and it was perfect for couple days until this morning I tried to start it and it was a little cold in the car and it wouldn't start. It did the same thing. It finally started and I drove it around for a little while with heat on. Turned it back off and started it back again perfect after it warmed up.
why won't it start when it's cold? The lights come on and everything when I turn key to right but won't start. Only when it's cold it won't start? Anyone know what might be wrong with it?