Laptop doesn't boot properly if shut down while on battery power

The company I bought the laptop from wants me to send it to them for repair or replacement, which is fine, but I’d rather avoid the hassle and lost time if possible.

The problem is: If I shut down while the laptop is on battery power (as opposed to AC power through the adapter) then when I power it back on, the laptop won’t boot properly. It gets through the “starting windows” screen then goes to a blank screen. (Black, though not completely off. Like really dark grey, I guess.) The computer is inoperative at this point.

I can then start it in safemode, do a system recovery to the latest restore point, and all is well.

(And to be clear: If I shut down under AC power, then there is never any problem booting up at the next powerup.)

The diagnosis from the people I bought it from is that there’s a video card problem or a video card driver problem. (?!) I uninstalled and reinstalled the driver* and that didn’t fix it, so they said to send it in.

But doesn’t this sound more like maybe a power management problem?

Any ideas?

*There were oddities in the video driver uninstallation/reinstallation process, too. I can completely uninstall the driver (it’s an ATI Radeon 5850) and the Catalyst utility. But then when I try to reinstall the Catalyst utility, it basically, as far as I can tell, goes through the motions and then completely fails to have actually installed anything. If I then restart the computer, I can’t prevent the computer from immediately loading up an old driver. I am then able to install the Catalyst program, and from there install the newest driver–but that doesn’t seem ideal since I’m thereby installing over the older driver instead of installing the newest driver fresh on a completely graphics-driver-uninstalled machine.

This didn’t seem to bother the tech guy I talked to so maybe it’s nothing. I just thought it was supposed to be very important not to install a graphics driver over an older driver, but instead to make sure all graphics drivers are uninstalled first.