Not much you can do at present - but I would keep on at the hospital / HR dept / trust CEO if required! Assuming this is on NHS land, they contracted Parking Eye and should be the master in the arrangement, penalising your own staff when the carpark is out of order seems particularly viscious.
You can ignore the scary looking letters from DCBL, they are powerless and just trying to frighten you into paying. Eventually you will receive a letter of claim, and then a court claim. As long as you defend it, for which advice can be provided, it will almost certainly be discontinued before a hearing.
If you can, post up the original PCN and any original or POPLA appeal and correspondence. Come back if / when you get a letter of claim as that is usually worth a reply.