I can't say from the facts stated whether or not the output transformers are blown, or if something else could be causing the problem. However, I would make two points:
1)Whether or not damage will result from powering up a tube amp (that has output transformers) and subsequently powering it down without having anything connected to the inputs and outputs depends on many aspects of the design of the amp. Experience with a different model amp has no relevance.
2)Regardless of whether or not damage might result with a particular amp design, IMO doing that is ALWAYS bad practice, especially if shorting plugs are not used on the inputs. In addition to the possibilities that have been stated, turn-on or turn-off transients could in effect put a signal through the amp. That is particularly likely to occur when the amp is being turned off, if shorting plugs are not connected to the inputs. Transients generated at the instant the power switch opens could couple into the inputs of the amp (to a greater extent than they normally would, because of the high impedance that is present at that point when the inputs are unconnected), then be amplified through the amp's signal path, resulting in huge voltage transients being caused by inductive kickback in the unloaded output transformers (as described in the paper Jim provided).
How likely is that to occur and cause damage with any given amp design? Who knows? But IMO it is a risk that there no point in taking.
Regards,
-- Al