Easiest & cheapest way: Get a car adapter for your make/model of laptop.
Welcome to MP3car! If you want to power it with an actual power supply designed to turn the laptop on and off with the ignition and provide +12 for the screen and +5v for USB devices, you will need to look at something like the Carnetix P1900 PS in the store on this site.
To use this supply you will first need to identify the wires used on the Toshiba output side of the power brick. If you can identify that Toshiba uses "ID wires" like HP or Dell and you can figure out which wire needs B+ & which needs ground, you could then hook it up to the P1900 in a similar way that I did it using the standard house current adapter that you already have. See post #7 & #8 of my work log linked below for more details on this.
The other option is as Darque stated above; just buy a 12v car adapter for it. The third option is don ;t drive any further that the battery will last
My 2007 Ford F350 Work Log located HERE