You're going to need a trunk full of batteries.
OK, I might be exagerrating a bit. A second battery and a low-power laptop might be able to stay on for that length of time.
You're going to run into a couple issues, though.
As the battery drains and is recharged, it will lose storage capacity. It's the way batteries work. This means that over time, you're going to be able to leave teh comptuer running for shorter and shorter periods.
I think your goal is attainable, but not without some careful engineering of the power situation. And even then, I don't see the practical purpose of leaving it on all the time.