Hi,
I appreciate the original thread is from 2017 but posting as this might help others.
I bought a secondhand POD HD400 advertised with "no sound" error so I got it cheap. I was hoping to fix it and use it. What I noticed was after time the sound came back, similar to the OP however mine took 12mins (I timed it 3 times). I read and noted that people with a similar issue had changed preamp caps under the guitar input shield however an audio signal trace showed audio was getting into Codec 1 (cs4272) and out to the DSP chip, but not coming back from the DSP Chip. When the sound did come back everything worked fine. If I turned it off and straight back on again it took another 12 mins for the sound to come back so I kinda ruled out heat / solder joints because the unit was already warm. Instead I was thinking software / firmware, an internal boot issue taking the same time each startup to unravel. I performed a factory reset and this has fixed the issue. If doing this remember to back up your patches. Try this before opening the unit up as it may sort you out. Good luck.