well, here are my advices:
- In case you remouve the batt. i think the 7815 is ok.. i think i was wrong about saing it wont work, but use a good heat sink it will help it deliver all the current you may need.
- About remouving the display, i was suggesting, for the sake of your laptop, you can just connect your LCD to the parallel port of your laptop, and leave your screen as it is, as you may need it to start/stop your program, or use this laptop in another projects later...and taking a huge PC screen with you is not that funny! you could just turn off the laptop's screen. most laptop have this feature.
but i think you are approaching to a realiable solution...
good luck.