There is a 125V, 20 AMP line fuse inside the microwave. Its usually mounted on a small input line filter board at the point where the power cord enters the back of the unit. You will need to UNPLUG the microwave oven and remove the exterior case to access. The case comes off in various ways depending on manufacture and model. Searspartsdirect.com has some excellent exploded view parts illstrations you can use to assist you in component location and assembly.
If the model number is correct, the fuse is listed as item 55 in this parts illustration:
There are also a couple of thermal cut-outs listed as items 51 and 52. These can affect the operation of the oven as well, but usually are related to overheating something in the oven cavity. If you haven't overheated the oven cavity recently, its probably the line fuse. (Popcorn and Potatoes are notorious for causing overheat problems).
You can purchase repacement fuses for appliances at any hardware store. Just make sure the rating is the same as manufacturer installed fuse. You need to purchase a 125V, 20AMP, slow blow for best results.
To answer your question about the fuse blowing when the unit is not in use...Yes, this does occur. You may have experienced a minor power fluctuation such as a brown out over the night that could have caused the fuse to blow. Some components are more sensistive to variations in current than others.
Another possibility that I have to mention is roaches. This does not in any way insinuate you live in filthy conditons, or have an infestation. I just need to mention that insects (such as roaches) are attracted to electronics. Especially, where there may be food. Since their body composition is mostly made up of water, if they crawl across an electrical component, they could cause a short circuit and blow a fuse.
If you have any questions, or need assistance troubleshooting, please post back and let me know. I hope you find this information helpful.
NOTE: Make sure you take any resistance readings with the microwave UNPLUGGED and the component under test isolated (removed) from the circuit.