Audio Amp:
Try thisAnd a quick guide on using itLCD Driver:
Send them a message asking about your screenSwitching it over to LED will just make things more complicated for you, and it will look worse.
As far as using the battery, I wouldn't. If you have room to leave the compartment after shoving in the hdd, power board, lcd driver, and audio amp; I would rebuild the battery to your own specs. For about $150, you could get closer to two hours out of the laptop, and get rid of most of the problems that those older battery packs have.
I would also get a piece of plexi or other plastic and cut it to they keyboards shape to smooth out the inside of the laptop a bit. You could do some pretty awesome things with windows if you have the patience for it.
Finally, i think that fan is blowing the wrong way. Generally, you run a heat pipe from the main heatsink to one on the flat side of the fan, and have the flat side going to the outside. however, if you are taking out the keyboard and putting plastic there, it would be easy enough to guide air out the top of the laptop if you have if facing that way.
As far as the PSU goes, I'm working on something, and if I get one designed, I'll be sure to let everyone that's watching know. TI.com is a good place to start.