Will not cold start

[dsmDolney]

Bought a new battery. Cranked and cranked finally started rough. Ran fine after about a 20 minute warm up drove it to get gas and threw a check engine light. Started back up when it was warm but sat over night and didnt start in the morning . looked at it today coolant temp switch wires are out of the plug. Would that make a non start issue. Any other reasons why it wouldnt start. Domt have a laptop to plug into to check the code