You're kidding, right??
Q10 is a mosfet. You'll need to probe around or make friends with a good Tech to figure out a suitable replacement based on its size and its markings, which look like "Z2" as far as I can see. Since most of the other mosfets used in the IOpener were manufactured by Vishay, it's likely that you can identify the part in one of their product catalogs.
Chances are fair that replacing this chip will restore your LCD backlight, since mosfets often sacrifice themselves to save the rest of the power circuitry. If you really did blow the fuse, you should replace that, too.
If your skills are up to it, you can desolder the old chip with some flux, solder wick, and a 15-watt soldering iron. Otherwise, dremel through the chip to separate the pins, and desolder each pin one-by-one. I don't recommend wire-cutters, as they sometimes pull up traces.
The good news is that your IOpener is still functional. I suggest looking up the VGA connector's pinouts, and fashioning a cable that you can hook up to your VGA monitor -- at least you'll have some functionality while you're figuring out what to do about Q10.
