I had this I recall it being caused by frequent cold shutdowns; the battery being loose due to the Mugen cover & double Scud connection issue, one day the LED was stuck. I don't think it was lit when powered off, it has been a few years now so I dont actually recall. Nothing I could do fixed the problem and it drained the lifetime of the battery significantly. I desoldered the surface mount LED and used that N900 for another year or two when I think the MMC corrupted or the no-SIM happened. There was enough backlight form the others to use the KB after removing one LED.
I think you could even fix the problem as an amateur by destructively crunching the LED with a needle nose pliers if you don't have a hot air rework station or soldering iron and the basic skills to use them to desolder surface mount components.