RM9 won't turn on - switch?

 I'm not familiar with your amp but there is a good possibility that a failed tube took out a resistor or fuse in the bias circuit. 

IIRC, there's definitely glass fuses in there somewhere. I owned an RM-9 25 years ago and remember having to replace fuses. On mine they were right out in the open, in chrome-plated fuse holders.

Yes, there are 3 fuses. 2 (1A) fuses (probably in the bias circuit) and a 5A fuse which probably is in the filament circuit. They looked good but I will check with a meter.
The filaments don’t light which is why suspect problem in the mains.

The 5A fuse does affect the lighting of the filaments. If this fuse is blown the amp will look like it is off. The 1A fuses (one per channel) affect B+ only. If one is blown you will not be able to bias the output tubes for that channel, but you can still balance the drivers.

Sounds like you have a MkI and the issue could be the power switch as well, especially if you have the square switch which will fail. The rectangular switches were much more reliable. Check the connections to the switches as well.