When you swap in different Pt2399 chips, do they all get hot when you apply power to the circuit? Does your voltage regulator get hot? I think you need to check the parts that connect to that chip for either a short from a solder bridge or a bad connection. That also likely explains why there is a problem getting any sound from that part of the circuit.
follow the suggestions you will see in many forum posts --
remove board, jacks and footswitch from enclosure
see if it works out of the enclosure (unlikely to make a difference here since you have dry signal already, but still worth checking)
post detailed photos of each side of the PCB, the in/out/power jacks, and the footswitch so the wired connections are clearly visible
If you only have dry signal when the board is engaged, you are not getting sound from either the PT2399 or the Belton brick. look at the schematic and concentrate of the part where the audio signal separates to go to those two chips up to where the audio is recombined with the dry signal. if you are not able to sort that out I suggest putting in a little time about learning to read schematics since that will benefit you every time you are troubleshooting a problem in a build.
You most likely have a bad solder connection or short that is stopping the sound either going to the delay chips or coming back from the delay chips to be mixed with your dry signal. you can use your DMM to check the connections between the parts in that part of the schematic, but it may be simpler to build an audio probe and start tracing the audio from Pin 7 of IC4 to it connects to the PT2399 and then through the Belton brick and parts to Pin 6 of IC1.