My IT support experience suggests to me that your user is lying, and that the laptop's problem results from keyboard matrix damage caused by user carelessness, most likely involving a beverage of some sort. (Leaving a laptop unattended, with a beverage nearby, and small children or pets present in the area, counts as "carelessness" for the purpose of this explanation.)
Try plugging in an external keyboard and see whether it also produces the misbehavior, which it won't, thus confirming the problem is specifically with the inbuilt keyboard. (You already know it's not a software problem, because you wiped the disk and reinstalled everything. A software problem wouldn't survive that process.)
Dismount the laptop's inbuilt keyboard and examine it to see whether you can tell what got spilled in it, and also check to see if the spill made it to the motherboard. Assuming not, replace the keyboard with a fresh unit off eBay, give it back to the user, and ask them to be more careful with their coffee/soda/whiskey/&c. next time.