Ok Guys, I think I found another solution for Function keys that stop working and backlighting that stays dim regardless of whether it is running from batteries or AC -- upgrade the BIOS.
I have Sony Vaio PCG505 (something like that, is at work) and for a YEAR I couldn't see the screen if not running on AC power. I tried what many of you tried..the Sony hkxxx etc, etc, the Sony Library and many of the original and updated Sony drivers and still no change. Then as it happened my hard disk recently crashed, lost XP, saved data, and upon reinstall using vanilla XP the screen stayed dim irregardless of power source being used. I reinstalled Sony drivers and no difference. Finally I found a floppy drive that worked with Sony and updated the BIOS and full lighting and all function keys working! I decided to blow away the XP partition again and expand it out, and without any Sony drivers installed the backlighting and function keys stayed functional, so the BIOS change is what I believe worked for me, not any Sony specific stuff. Good luck -- hope this helps some of you.