Step 1: pressured air (inflow and/or outflow) with narrow nozzle. Should clean "unbound" dust out of the board and under the chips. Be very careful with buttons. I would not advise disassembling them as old plastic may crack;
Step 2: use shave brush to clear "bound" dust, and then use vacuum cleaner again to remove remainders. While using brush, be careful not to perform too sharp moves as bristle may get between pins or plastic parts and by tearing it off you risk damaging the components. Be gentle and use the bristle along its axis rather than perpendicular.
Step 3: use vodka. No, on the board. Do not use dissolvents. You can use isopropyl alcohol, but testing it on some area which is not exposed (e.g. on the bottom of the board). Aged materials (including silkscreen and colored polygons) may be subject to removal with spirits, thus if possible do not use spirit at all.
Step 4: keys can be cleaned by the soap and water, but that would be uneasy without pouring them inside the buttons. Be very careful, and use wet sponge a dozen of times on every button (instead of pouring everything into the water and then drying).
it has exhibited some unexpected behaviour
Cleaning may help here, but if issues continue after cleaning you will need to apply electronics specialist knowledge to find out the issue. However what you can definitely do after cleaning - taking magnifier and checking board and its components inch by inch looking for damaged conductors, cold solder joints and other damages.