I would bet the number of non-qualified people that have repaired or attempted to repair their microwave is easily in the tens if thousands. Yet I have never heard of a single death. Relax people.
Microwave working but not heating: Most likely the magnetron is bad. I wouldn't recommend replacing this part unless you actually know what a capacitor is and how to discharge one.
No power at all: Most likely the internal fuse. As previously mentioned above, follow the power cord into circuit board. Check ceramic fuse with an ohm meter if possible or just replace it. Replace it with the EXACT SAME fuse that you took out. It is possible that it took a surge and blew. It is perfectly safe to replace.
Internet search for your make and model, there are a lot of parts, schematics and diagrams available. Obviously buy from a reputable retailer.
NEVER EVER run a microwave without all the covers in place. The covers can possibly be shielded and that is what prevents actual microwaves from escaping into you, your family, friends and your pets.
So honestly, if my microwave had a blown fuse and I trashed it for a new one I would feel like I traded in my car because the battery was dead. We all need to minimize our disposable habits. Stay safe and use common sense.