Your mistake was in paying the first PCN. That marked you as a "mug". Nevertheless, you now have 4 more outstanding PCNs from NPC to deal with.
The debt collector letters from DCBL that have the added fake £70 per PCN added can be safely ignored. DCBL and any other debt collector has no power to do anything except to try and scare you into paying by using scary words. Ignore them.
The second mistake was contacting DCBL. Never, ever, ever, contact a useless debt collector. Don't waste your time. Simply ignore them.
What you now need to do is wait for a Letter of Claim (LoC) which is going to come from DCBLs sister company, DCB Legal, a bulk litigator. When you receive the LoC, come back and show us. We need to see if they've consolidated all the PCNs into a single claim or not. We will provide a suitable response.
They will eventually issue an N1SDT Claim Form through the CNBC which must be responded to. Again, show us the claim form when you receive it so we can provide instructions on deadlines and how to respond to it. The claim form, cannot be ignored unless you really do want to get a CCJ.
Normally, if these were for a single or maybe two PCNs, they would eventually discontinue. However, of a claim of over £600, that is unlikely. However, that does not mean that it cannot be won in court.
In the meantime, maybe you could go back to the location and gather evidence of why the driver did not know they were supposed to purchase a permit to park at the location. You say that the driver regularly parked there. Do you know when the parking restrictions changed?