The "Amiga III Technologies" keyboards are the ones manufactured by Escom that shipped with their A4000T, but they should be 100% compatible with the 2000, 3000, and (with a passive adapter) 4000 desktop.
Start by cleaning the pins on the connector plug in case they picked up some residue over years in storage. If that still doesn't work you'll have to move on to some more intense cleaning/repair.
Another diagnostic step: rapidly press the "broken" keys several dozen times or more. Do they eventually start working? I have an A3000 keyboard that sustained a wine spill decades ago and was never 100% cleaned (and I still haven't gotten around to fully disassembling it properly!

). Most keys don't work initially, but if they're pressed enough times they will eventually "wake up" - my assumption is that the physical action wears away enough of the residue on the membrane for the keys to make contact - until I don't use the machine for months on end and then need to repeat the process. All that to say that this might help you diagnose a dirty membrane compared to a more substantial electronic/chip/circuitry issue.