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.