Hi Aaron
Without knowing which state you are in or which private car park operator 'fined' you, I would not think paying would be a good idea.
With some car park fines the operators allege breach of contract and try to claim damages. However, generally the amount they claim is much more than their actual losses, and may not be enforceable.
In NSW, private car park operators will find it difficult to get details so it is possible to just ignore it.
See this fact sheet from Legal Aid NSW
http://www.legalaid.nsw.gov.au/publ...sources/private-car-park-finespayment-notices