Well,, yes,,, the keys on a laptop can pop out,, yo must be very careful when doing it, you can break the tabs (sticks) that hold them in. But it can be done and they can be put back if you are careful enough.
Since this is a laptop,,, this is the only thing you can do to check if it is the keyboard (which does sound most probable). Keybaord replacements can run about 20+ dollars, depending.
I used to know several very good, inexpensive laptop parts dealers, but have lost the names at this time.