What is causing 2000 Chevy Blazer to have starting-problems?

What is your question?

My Blazer is a 2000 and it runs amazing when it is warm but the minute it gets to be "winter," (ie it snowed for the first time yesterday) it won't start right away. Last winter I accredited the problem to the actual cold as this problem only occured when it had been sitting outside for a period of time. But I park it in a heated garage and the problem occurred this morning in the garage... It will "try" to start but then it shuts dow; it takes approx. 5-10 mins of "false starts" to actually turn over. I've replaced the battery within the past year. The fuel pump and tank were replaced less than a year ago. The "Security" light is on, and during the "false start" process I've found it somehow usefulto open the door in between attempted-starts to shut down the battery...? Any thoughts would be greatly appreciated.