Yup, Martin's almost certainly right here.
No glow in the power tubes means no (or not enough) current is going to the tube heater filaments.
Could be that there is a fuse specifically for those circuits which has blown. If it has blown, though, it's highly likely to be due to a fault in one of your power tubes.
Yes, no glow in the power tubes in standby mode indicate no heater current.
It is very rare that the heater circuit in an amp is fused (although the regs actually require that all transformer secondaries are fused...).
Assuming there is a fuse, when they fail valve heaters, like light bulbs, go open circuit, which wouldn't blow the fuse.
However if a valve has shorted plate/ screen to cathode this might blow the heater fuse, although you would also expect the HT fuse to blow too.
Although if not familiar with the inards of a 5150, if the constuction is the same as most other Peaveys then the heater filament wiring to the power valves is likely to be attached to the PCB containing the power valves via a Molex connector, and this can have worked loose.
Regardless this should be a very easy fault for a tech to diagnose.