2002 Starting Issue

[F350none]

This is not really a cold starting issue as much as it is a "if it sits" starting issue. If my 02 7.3 sits for more then 4 days you have to plug it in to get it started. If it sets less than 3 or 4 days it starts pritty easy. I have started it in 1 to 2 days in 10degrees with no issues and not plugged in but after it seting a week it will not start at 45degrees unless plugged in. I ran the battery dead trying. If plugged in it fires right up. I thought glow plugs but why does it start in 10degrees after setting 2 days without being plugged in. So I thought HPOP but why would plugging it in matter? Not sure. Any ideas? Not sure how it does at 70 degrees after a week of sitting it has not been that warm.