Why would you want to pay £100 when you are able to challenge the PCN? Also, it is not a fine. You must understand that this is just a speculative invoice from an unregulated private parking company for an alleged breach of contract. PE are not an "wuthority" of any sort and cannot "fine" anyone.
That appeal you posted above is not going to work. The NtK is compliant with PoFA 2012 and so, they are able to hold the keeper liable. n this instance, there is no point in denying you weren't the driver, unless that is the actual case.
From the limited photos you have provided, I cannot see anywhere on their signage that prohibits you from parking if the payment machine is not functioning. In this case, you can claim frustration of contract. However, it may be a little bit difficult to prove that you didn't attempt to make payment.
Should this go to POPLA (more than likely) you would be able to put ParkingEye to strict proof that their payment machine was fully operational at the time you were there. You can ask them to provide logs of the payment machines that show, at the time, other motorists were able to make payments. If there is a substantial gap in successful payments being made at the time you attempted to pay, that could be evidence that the payment machine was not functioning.
It all depends on how badly you want to fight this. If you're prepared to just pay £100 for the easy life, then that is your decision. If you feel aggrieved enough about losing £100 of your hard earned money because of a fault with PEs payment machined as there was no obligation to try and park elsewhere according to their terms, then you can fight this on the basis that no contract was formed.
Of course, there will be other points to put in an appeal, especially if PE reject your initial appeal, and POPLA is more likely to look at any points you raise such as the provision of payment logs to which PE will be put to strict proof.
