Is it the backlight (I'm pretty sure the 160 has a backlight), or is it the LCD itself? You could try cleaning or replacing the contrast pot. You could add a backlight or replace the existing one with LEDs or something. As for the battery itself, you can probably have it stuffed with new cells if you get the machine working reliably.
Overclocking to 33 mhz:
http://homepage.mac.com/schrier/spec.html
If you need something to write documents with, here's Nisus Writer Compact. It should fit on a 1.4 MB floppy no problem (remember to unstuff it on the Mac, NOT your PC):
http://www.tucows.com/download.html?sof ... 205066&t=2
If you need StuffIt Expander 4, just ask and I'll see if I can dig it out. I've got a bunch of that System 6 and 7 stuff around (sorry, I won't give away Word 5.1, PowerPoint 1, or Excel 4).
I recommend System 7.1.1. All Powerbooks besides the 100 and its cousin the Macintosh Portable need at least System 7, and 7.1.1 is as new as you should go with most of them. It
could run System 7.5.5, but there's not really any point to it and it would take up too much memory and hard drive space. Youc an find System 7.0.1 and an update <a href="
http://download.info.apple.com/Apple_Su ... /">here</a>, but they're 5 MB self mounting images so you will need to copy them to real floppies on another computer. Ideally, you should use another Mac, but if you don't have one around you can use Basilisk II.
Another fun toy is Backdrop, which can take any MacPaint document and make it your wallpaper. You should be able to find it around.
Let's have some specs! How much RAM does it have? 40 MB HD? Mac OS version?