A few years ago a remote that I had repaired with electrically conductive paint had something get stuck somewhere causing the backlight to indeed be on all night. This did drain the batteries, but also caused the plastic around the battery compartment to melt quite a bit:

I figure someone here would get a chuckle out of this. The batteries were really hot when I removed them. Also, the remote still worked for several years until I dropped it down a split level stairway. At that point the battery contacts broke off the circuit board