Will high volume setting blow an amplifier?

I'm not sure whether you are referring to an integrated amp or a separate preamp + power amp combination, but in either case it sounds to me like the underlying cause most likely was momentary loss of the ground connections between two components, while you were manipulating the interconnects.

If you lose the ground connections between two components (which are carried on the shields of the interconnects, assuming your components have unbalanced rca interfaces) while an inner ("hot") conductor is connected and the components are turned on, the destination component will see an abnormally high voltage. The exact value of that voltage will be dependent on many factors, including whether the components have two-prong or three-prong power cords, leakage currents in power transformers, other connection paths through the system, etc.

The volume control setting would only have been a factor if the part of the amp which was damaged was downstream, or "after," the volume control.

Regards,
-- Al

Don't know all the details, but it sounds like there was something wrong Before you set the volume control at 50%. Just because the gain setting was 'high' - that shouldn't damage an amplifier. (Speakers can be damaged like that). The 'loud hum' you first heard was not normal, and leads me to believe in a "preexisting condition".