If you are indeed getting some LED light in every row (or at least, almost every row), then the AVR microcontroller is indeed running and scanning between the rows. If so, it should be possible to reprogram it, and that’s a separate issue.
If pushing down on the socket improves things, then either the chip isn’t fully seated in the socket (and check the others, too!) or it’s not soldered correctly. At this point, a soldering issue is the most likely type of thing that’s going wrong.
