2004 Chevy Trailblazer won't start and key fob doesn't work but other

electrical systems work fine? On cold days my 2004 Chevy Trailblaer has not been starting. When I come out ot the truck, the keyfob to unlock the car does not work. I unlock the door manually to get in. When I turn key all electric systems come on but no crank. I can hear the fuel pump running. Yesterday I played with it for about 10 minutes and it finally started. Today I could not get it to start. Any idea what it could be? I am good with cars but this is stumping me because once it gets a little warmer by the afternoon or after it has been running there are no issues restarting it. Thanks for your help.