Biggest prob I see is that your laptop is a power hog. The runtime on the provided battery from the spec I saw was 2 hrs on a 1400mah batt. Which works out to about a 75watt battery or so. (based on the 19.5v) To get double that (say 4 hrs) you would have to go to 2800mah (2.8ah) The most inexpensive route would be:
Get a 12v 20AH SLA battery (as you are only going to get maybe 80% usage, real life is prolly closer to 50-60%) (weighs about 10lbs, runs about $20
Get a cigarette plug (female side from radio shack) $5-10?
Get a car adaptor for your laptop like suggested before. $80ish?
I would not suggest using 7ah batteries. Because of the fact that you are using a transformer to "up" the voltage, it is going to be very dependent on the voltage staying round 12v. With the smaller capacity battery it is not going to stay there very long with any kind of current draw, plus you indicated that you want to run other stuff off of the battery. It might be argued that running 7ah batts in parallel (plus connected to plus, minus connected to minus) is more convenient to carry and will get you about 14ah, but it will also get you more connections to worry about.
If you want lightweight, don't care about price, and don't mind that you are only doubling your capacity (adding 2-3hrs) look here
http://www.lindelectronics.com/cgi-bin/store/shop.cgi/!ORDERID!/ppack/MP60-3-sony/dbx_gen_detail_product $350