If that brick is the one that came with the pc (ac power plug on one side, 19v output on the other) then you probably want to cut it off between the brick and the pc, since you no longer need the brick, as you will be powering the pc with dc voltage directly.
As for the cig lighter outlet, let this image speak for itself.
Connect directly to your battery through a properly sized fuse. Do not use your cig lighter outlet for powering a pc, even a small one. You have been warned
Credit, as always, to 2k1Toaster for that image.