Make a new patch in an empty slot with no FX, just an amp, any amp, don't change anything, strictly default. Guitar in to POD, left 1/4 out to the Peavey channel A input. Make sure you are plugged into the outer Neutrik connectors not the two center 1/4 jacks. Peavey channel A out to Blackstar cab. Check to make sure the Circuit Breaker on the back of the Peavey is not tripped, reset it if it is.
POD Master full clockwise, Peavey channel A volume 1/2, channel B volume off. By the pedal on the POD, GUITAR IN to Normal, 1/4 OUT to Line. Guitar Volume 1/4 and see what you got. You should definitely have sound now. If nothing, turn Peavey off and switch to Channel B and see what happens.
If still nothing, plug your guitar straight in to the power amp and see if there is sound. Keep the guitar volume low and amp volume 1/2 at first so you don't damage anything. Turn guitar volume up slowly. Check both channels.
Let us know how this works and we can go from there.