Audioquest

Today as always in teh winter, I go start my car and let it warm up for 10 minutes before getting in and going to work. This morning however, I came out to go and it wasn't running.

I turned the key and just a click like a dead battery, however I know it's good and a brand new alternator.
20 minutes later I try again and it starts jsut like it always has. No warning lights, it's all looking ok.

I get about 3 blocks, some of the dash warning lights intermittently come on (seat belts, theft, etc), the headlights dim and the car stalls. Now it does the same thing, clicks but no start.

Any ideas on what it is, or maybe where to look to see if there is a loose ground or power wire that pretty much powers the whole car?

Thanks for your help