I am assuming this is a Mark V90? If so, you can leave the FX loop in active mode on the back panel, it is the same switch that places it into hard bypass. So turn it on. Then select the FX loop channel, you can leave it set to FS for now. Play through the amp as you normally wood, if that works, it is likely the V6 tube is not the issue. Since there is a relay that will disconnect the internal jumper on the FX circuit, try changing the rotary knob for the FX assignment to all channels. This will activate the relay. If there is nothing in the FX jacks, you should still have some sound since there is an internal disconnect in the return jack. If no sound, do as what Dom had recommended. Insert a jumper in the FX send/Return jacks. When ever the amp is placed in the FX active mode (not the hard bypass mode) the V6 tube will be active and the output volume master will do what it is supposed to do.
If that works without the footswitch connected, and then when you install or connect the footswitch, you may have a bad cable, (check to see if it has all 8 pins). Also since the Footswitch also has a mute circuit, there could be an issue with that circuit in the cable, or the footswitch. If not mistaken, I believe the front panel has a light for the mute when it is active. It is right above the standby switch. If that turns on when you plug in the footswitch, I would assume it is footswitch or cable related. The front of the amp has a pull switch on the solo control, if you pull it out it also puts the amp in mute. I believe that is the same circuit. Sometimes all it takes is a few turns on the rotary knobs on the back as the movement cleans the contacts. I believe they are sealed switches but I could be wrong on that. May as well pull out the solo knob a few times. Not sure on the other Mark V amps like the V:25 or V:35, I am not sure if those amps have a mute feature or hard bypass function.