The one most common fault in any microwave oven (aside from the fuse) is a bad door interlock switch. There are two of them, and they are relatively easy to replace, and can usually be purchased at any leading electronics parts supply. Also check the wire connections to those switches; often they show signs of overheating, and simply need trimming and reconnecting with a new connector.
Repairs beyond that are out of the realm of the DIYer, as they involve replacing capacitors, HV diodes, magnetrons (unlikely), etc.
I'm assuming that the fuse is good, as you say the unit does appear to have power.
1998 Triple E F53
1995 Jeep Wrangler toad