Got a new keyboard this week and a bunch of keys aren't working, or not working very well. Specifically, num 4, 5, 6, 3, end, A, J, K, ;, Z, C, <, ?, and right shift. The board is pretty old though, and the connector is a bit dirty:

The soldering also looaks somewhat weird, but not specifically around the switches that are dodgy. I don't think I can open the switches to look inside.
What kind of problem does this sound like? Connector, soldering, or switches? I'm not sure why it's these specifically. Anyone have any idea?