Strange laptop keyboard problem

Recently (that is, within a number of months ago) whenever I boot up my laptop, the qwerty row of my keyboard doesn't function except for a few choice characters, like t,y,],[, and \. If I let it sit for a while, usually at the login window, the keys will eventually start working again. If I get impatient and use the onscreen keyboard function, it seems like it takes longer for those keys to work. The problem seems to get worse when I run the laptop off the battery instead of through the outlet.

Does anyone have any idea what could have caused this, or how I might get it fixed? It's a laptop so I'm not particularly hopeful that it'll be an easy fix, but I am pretty curious as to how this sort of problem could start in the first place.

Jam it back in, in the dark.