The parking company is VCS, not IPC.
Are you the registered keeper of the vehicle? (I.e. You hold the vehicle's V5C document) And did you reveal who was driving in your appeals? If so, it's a shame you didn't come here first, as that notice at least was issued too late to hold you liable as the keeper.
You'll not have debt collectors knocking at your door. But VCS can be litigious, so if you don't settle with them then there's a fair chance they'll take you to court, especially with 4 charges in play.
The £680 total means that DCBL have added on their spurious £70 per charge debt collection fee. This could be challenged in court. On that basis, one option is to offer VCS the original charge amount (£100 per ticket), pointing out that if it were to go to court the extra £70 would likely be dismissed.
Any photos of the signage at the site?