A shorted heater means that possibly the filament leads inside the tube have shorted. It's not very likely this could occur but if it did there is a fair chance it would prevent the other tubes from lighting up. My guess is you have a bad resistor or some bad diodes.
I read your other posts about your Cornet dying. Does your fuse blow if there are no tubes installed? If so you may be correct and have shorted some diodes. Yes, the RadioShack diodes will work.
To test the transformer, you might consider un-soldering the output leads from the PCB and measuring the output voltage. Obviously use extreme care since the high voltage leads are 550V!
If it were me, I would un-solder just the green wires (filament circuit) and see if the fuse still blows (all tubes removed). If it doesn't blow, then measure the voltages out of the transformers where the are soldered to the PCB. Much safer than having the wires disconnected.
It's also possible the rectifier tube somehow shorted and is causing the fuse to blow.
Another thing to check is C11 and C8. These caps are across the secondaries of the transformer and a short would certainly cause blown fuses.
Speaking of VSAC, I haven't read a single report of the show.
Good luck on repairing your Cornet. Jim will certainly be able to offer better advice than I but the above items are likely the prime suspects.