If you load a text editor from WorkBench (say ED or EDIT), and try every key in turn, some return incorrect characters?
So far, it sounds like the keyboard controller chip (the large chip next to the LEDs) has taken a dive. This has happened to me before.
You can replace the keyboard for a modest price from eBay. If you get one that is undesirable in some other way, you can simply swap chips.
Note: you want an A500 keyboard. They are easy to find. The A600 and A1200 do not have this chip on their keyboards.