It's been years since I had my first electronics class in college, and unfortunately I never really had a chance to use that knowledge.
My laptop is rated at 19V at 3.42A, so the W is about 65, right? So powering it for 6 hours would require a battery with a capacity of of at least 400W. I was thinking of going with an AGM battery at 12V. As for the solar panels, I was planning on lining the roof of my car with them. I've seen some 6"x6" panels providing 3W for under $10. 8 panels could fit on my sunroof and could recover about 5 hours worth of usage (on a good day, not accounting for actual draw of the system itself.)
Obviously I'll want a battery with a high enough capacity that running it for the target of 6 hours doesn't take it below 20% capacity. I'd like to include a circuit to monitor battery life, and will have to include a way for the power from the solar panels to be dissipated if the battery is fully charged. To make things simple, I'm considering using a COTS DC to AC inverter, so that I can simply plug my laptop into it (or any other device I might want to use)