Losing individual speeds is *almost* always resistor failure. Not always, though. It can also be the fan switch or its harness connections burning up. If it is the switch, it's replaceable individually without having to buy a whole new control head, btw. But yes, your first suspect there is the resistor.
Now what caused the resistor to go bad? Sometimes it's the blower motor going bad and drawing too much current. Now with your fan completely out I'd suspect the motor itself or the power/ground connections to it as they can get oxidized and crap out.
So start with a test light or better yet a multimeter, see what your readings are at the power/ground connections for the blower motor, with the fan setting on high, and let's go from there.
Richard