you could go for a run and see if anything's been written to the card, that may help with diagnoses. you have tried turning it on and off a few times I assume?
How about the screws on the card flap, any sign of corrosion?
n-wal when you say you can't turn the backlight off, do you mean you can't turn the gt11 off?
If so this is an indication that the internal computer has crashed. 2 options, leave it until the battery runs out, recharge and try again, or undo the cover and disconnect the battery for several seconds, then reconnect it and try again. While you have the cover off have a close look (magnifying glass) for any internal corrosion. I know the screws are external to the seal, but several units that have failed have corroded screws. Maybe people take the card out with wet fingers?
Well I couldn't turn it off, then after some hours I could. I put it on charge for a couple of hours but the charging icon didn't appear. Now when I try to turn it on the light blinks and the backlight blinks on and after a bit turns off. That's all I get out of it.
I will try disconnecting the battery as you suggest.