Hope you get that sorted - that's a major, major bummer. Does the system actually run at all? I just received a junk Dell Inspiron 8100, and another Vaio PCG-FX601.
The Inspiron 8100 did initially power off of a battery, but then stopped doing so altogether after that battery flattened itself, even using other batteries. It wouldn't power from the AC, nor would it charge a battery. However, I've pinched the palmrest, keyboard and screen from it for my Inspiron 8000, so it was worth the price I paid for it (I'd have pinched the GPU if it was the ATI Radeon Mobility chip; sadly, it wasn't. No idea about the CPU; when it did power on, the keyboard wasn't connected) I wasn't amused to find it protected by mere newspaper though!
The Vaio PCG-Fx601 is an odd one. As far as I can tell, it works perfectly... apart from the fact that there's a loose connection somewhere in the screen, which causes the backlight to conk out if the screen is nudged. It's not a bad backlight, because the screen will stay on for many minutes if the system isn't knocked, and I did improve it a fair bit by reseating every cable in the screen (including those behind the bezel), but it still hasn't sorted it. A little miffed that the seller didn't mention its lack of a HDD caddy/cable, but it was 99p before P&P, so... The screen, when not glitching out, is actually in very decent shape; the system seems to run fine off of a bootable Linux CD, with a functional trackpad, good speakers and a good DVD drive. It's certainly not overheating either. Battery also charges and holds a charge, but yet to evaluate just how good it is. Not yet sure if I'll keep it as spares for my main Vaio or fix it up and sell it on.