solid state power amps

Not any more a characteristic of SS than tubes.
If the amp is buzzing it sounds like indeed a transformer. I owned 1 amp that did this after a year. Another one, same brand has been quiet for 10 years.

transformer hum from ac line

google "van alstine humdinger' - built to solve frequent causes of hum problems in hifi systems

I’m not kidding. Unplug everything and plug it back in a few times. If anything looks dirty, clean it up. If it is loose tighten it up. RCAs, XLRs, PS cables, check all the connection at the speakers, again plug and unplug, or loosen move the cable and retighten.. If your main plug is on a TWO outlet plug, unplug, clean tighten and swap outlets. Remove the fuse holder, don’t touch, inspect, clean (unless it’s a fancy fuse DON’T clean) and or replace and reinstall.

You can't make it go away by pressing on the top of the case or anything? Mechanical noise or actual transformer noise.. It didn't come loose, or something? Hand on the transformer?..

Cost nothing.. Always a good idea every now and then. It depends on your area, your environment, ay..

Regards

Transformer hum. Could be the transformer needs to be tightened. Or could be a design flaw where the transformer vibrates in its mounting or to the chassis.

Or as stated could be that DC has contaminated your AC line.
Is this a low-level hum?

Many threads on here about transformer hum.  Sometimes it's easily cured, sometimes it's impossible however heroic the efforts.

Transformers have no moving parts but they do have alternating magnetic fields due to the alternating AC current and so they can vibrate. Its usually small and silent when the alternations are balanced but even a tiny little bit of DC offset can make enough of a difference to cause it to vibrate to where we can hear it. A lot of DC offset and you need a DC offset eliminator. Or it can be so tiny the tricks oldhvymec suggested will work. Cleaning contacts and all the rest are all great things to do anyway. 

As much fun as it would be to tell you yes this is a solid state thing you need a tube amp sorry, not true. You do need a tube amp but for another reason called sound quality.

It is possible that another device on the same circuit as the amp is causing noise or hum on the amp.  I had this with fluorescent lights and their ballasts.  I changed to new ballasts and the amp became dead silent.  Another source can be lighting dimmer switches.

Can you tell if anything else is on the same circuit?  

Depending on the hum, yes, it could be transformer or ac line noise.  One is cheaper to resolve then the other.   I would call Victor or Steve at BAT. Have them give you some suggestions.
Good Luck!