Since the most likely problem with the transformer would be a primary winding that overheated and burned open, I'd unplug the thing and use an ohmmeter to first check across the power cord hot and neutral prongs with the power switch in the "ON" position. You should see a pretty low resistance, say under 50 ohms. If it's open circuit (infinity on a VOM or O.L on a DMM), then check the leads that are fed to the transformer from the mains circuitry (probably go through the power switch and/or a fuse or circuit breaker) and check their resistance. Should be the 50 ohms. If so, the problem is with the wiring to the primary whether it be the power switch, fuse, circuit breaker, line cord or the wiring itself. If the infinity reading, you have an open primary. It's likely not easily repairable since the primary of and E-I core is wound on first and the secondary on top. If a double-D core, you might have a better chance, but still only if the open is on the outer layer of the primary winding.
Dean