It seems like this transformer is dead. Is it worth it to try and replace the heat fuse (that it may or may not have)? I think I'd rather just replace the whole thing. Any thoughts on this or finding a replacement based off the schematic?
Sorry, I do not understand your readings, my mistake as it looks like I did not specify exactly what to look for.
If your meter is digital, and you are measuring resistance, it will read close to zero if the windings are good, and "OL" or something similar if it is bad.
From the manual, you have the multi-voltage (E-Type) transformer, that explains the 3 primary wires. As you are in Texas, the voltage select switch should be set to 120V, and the primary winding you will be using is the Yellow-White.
So, with the power disconnected, if you measure between the yellow-white wires do you get close to zero ohms? Or is it an open as if the meter leads were not connected to anything?
If it measures open, the transformer primary windings are bad, if you get a resistance reading, the primary winding is good.
If the primary winding is good, then test the secondary’s by connecting the power, turn the unit on, and measure AC VOLTAGE between the red and black wires, then the yellow and orange wires. You should have readings, if the windings are good. If you don't, disconnect the power. Disconnect the secondary red wire, (make sure you note where it connects, pictures are great here) and measure resistance between it and the black. Then do the same with the yellow and orange.
Here again, if the readings are close to zero ohms, the windings are good, if they are open, they are bad.
The thermal fuse you refer to will be on the primary winding if it is there. Replacing it will be a problem as they have never really been easy to get. You will need to know the temp and current ratings, or if you are lucky, there might be a # on it. Not a great hope of finding a replacement.
The transformer, a quick Google search for the part #L01-2776-05 pulled up
http://www.encompassparts.com/model/KENBASICC2/_/_/Kenwood/BASICC2/
Don't know if it is available, but maybe.