[Eliot Ness]

Yes, you especially need to replace the electrolytic capacitors, they are #47 on the schematic, as well as all of the wax caps. 

There is a chance that your transformer was OK, but a shorted component, which is most likely an electrolytic capacitor, is causing the short and overheating/sizzling.  Unfortunately, even if the transformer was OK, if you let it sizzle long enough odds are it might now be bad.

So, like Mike said remove all loads and measure voltages. Then do not power it up again until all caps have been replaced and the tubes checked (especially the 84 for shorts).  Maybe you'll get lucky and not have to buy a transformer.