Starting issues

[screwd08]

Yes I know another starting issue thread. I've done a lot of searching and found similar problems but non quite the same. So the story goes:

A month back I noticed my car struggling to start a little when the weather got cold. The car ran perfectly fine during the summer and fall. At the end of December I went on a vacation and while on vacation we got hit hard with snow on the east coast. About a foot or so in my area. I get back right before I have to go back to work and go to start the car and it wont start. Its turning and sounds like it wants to start but it wont. I gave it a little gas while trying to start it and it fired right up. Let the car warm up while I finished what I had to do and only to find out the car shut off. Try to start it and no go. Came inside and researched some and went back out and it started. Let it sit for awhile and it shut off. Where should I go first about trouble shooting? No codes being thrown and sorry for the long story.

The only things done in the past year to the car was a new battery, upgraded alt to a quest, and during the summer got rid of the marble in a can sound. Plugs and wire are good.