is this small board full of chips?? If not, try to find any transistor (black half-cylinder, with writing on the flat side, with 3 "legs"), this should be what you're lookin for, an amplifier for this small thingy-speaker.. You need to change it to a new one..
The other problem might SMD mounted components, or an amplifier "hidden" in some chip..
-I won't give my hand that this is the problem,
-don't know anything bout microwaves ovens - except how to cook pizza in it..
-soldering ability required!
You should really consider visiting some service - they'll know what to do..