If that doesn't work how can I pay the original charge, do I go to enterprise or Hounslow?
You can't.
If you are locked out of your Enterprise account and otherwise do not have the prescribed evidence, then I'm sorry but there's nothing you can do on your behalf*. As explained, the PCN is addressed to Enterprise and only they may respond. They had 3 choices:
To pay and charge you;
To make reps on the grounds that they are a hire company which, if accepted, would lead to Enterprise being off the hook and to you getting a PCN in your name;
To authorise you to make reps on their behalf.
They've done 3 conditionally but because you missed their deadline they opted for 1 and paid.
It now appears that they're unable to recover this directly from whatever payment channel they planned to use.
What they do now is up to them, but their choices lie in contract law, not parking regulations.
*- I suppose you could just write to the council and declare yourself as the hirer and would they please deal with you by issuing a PCN, but they'd be foolish to act upon this because it's procedurally improper and would allow you to challenge successfully any such PCN