Over a year later, I've finally fixed it! It's caused by a BIOS problem, and it is reasonably easy to fix. First of all, make sure you've got the latest BIOS configuration. You can download an official BIOS flash program to do this. You should download an EXE file, which you should save to your computer somewhere (e.g. your desktop).

Close all other programs, and then double click that file. (You will need to be running on AC power, not the battery.) It should do everything necessary to update your BIOS, and it will ask to restart your computer.

Not done yet!!!

This is really important. Flashing and updating the BIOS is not enough. When the computer starts rebooting, you will see it offering you the chance to press F2 to load the setup. Do this, and the BIOS setup program will load. Navigation with the arrow keys on your computer, and go all the over to the right-hand menu option. Select "load optimal defaults", and then exit saving your changes.

Your computer should reboot, and that will be it sorted.

You can check that it's worked by loading