my laptop kinda died

Here's a trip update! Scroll down for the trip in review.
I'd almost forgot about this part of our last trip.
Usually I get up much earlier than Craig, so I take my laptop along and play games in the morning. But this last trip, my laptop would not work. I'd plug it in, turn on the power, I'd see the keyboard light up and could hear the fan spin up. Then after about 5-10 sec. the fan would power down to low, and then another 5-10 sec. the laptop would shut off, then immediately restart. It would continue this same pattern until I unplugged it. There was never anything on the screen. It wasn't on long enough for windows to load. Does any of my computer savvy readers have any ideas? I'm thinking maybe the power cord with that big box thingy on it might be bad. Maybe it's not getting enough juice to keep running. Does that even sound possible?
I don't have a battery back-up, because the battery died 2 years ago. Probably because I only use it on trips, and it sat all the first winter after I bought it. I didn't know I needed to plug it in regularly to keep the battery charged. And I never replaced it because I always use it in the mo-ho where we have power and I always plug it in.
Anyway, any ideas would be helpful.