the fact that some keys are not working, especially a pattern is a very good indication of missing connections.
I assume some pads broke off during desoldering. Can you check this with a continuity tester?
Especially the following connection:
Pin4 of the CPU to pin 6 of IC57 (this is deduced from your key-pattern)
The same line would also be responsible for the faulty range switch.
You can just plug it in the socket, yes.