The ROMs of that era cannot be flashed or modified by any means. If you're unsure if you WB disks are any good at all, just format a disk, run 'install df0:' to make it bootable and boot your 500 from there. You'll get a simple shell window where you can check the keys at least.
Possibly the keyboard matrix (within the keyboard) or the controller is damaged but before you start messing with the hardware rule out any software problem.
The clock time is provided by a battery backed up clock (realtime clock RTC). Listen to paul1981 and check the battery - they do leak after a couple of years and tend to eat through(!) the mainboard.
