I'm in Victoria so I'm not familiar with details of your legislation, but here are your starting points. Go to
Click on NSW, then Consolidated Acts, then alphabetical list, then R, then Road Transport (Vehicle Registration) Act, then Section18, where, behold!, you are in the sh*t.
Terms that are defined in legislation are usually in the first few sections or regs of the relevant law, but they can also be at the start of parts or divisions or just in a given section. "Use" may be defined somewhere. May be in another of the various transport acts and applies to all, or in regs if it's reg offence. Definition of use would probably need to extend to park or leave in road related area (which term is also defined) to catch you, otherwise it would have to be proved that you personally used the car when it was unregistered by driving it to where it was found. Probably a provision somewhere making the last registered owner liable, but you should find this as there may be exceptions that would help you.
There's also a similar offence in the Regulations. Don't know how your lot do it up there, but the penalty notice (which is what I assume you got as it's a fixed fine) should have a code number or reference to help you identify what you've been charged under, although that isn't easy to do if you don't know where to find things.
The penalty in the Act and Regs is 20 penalty units max.
Section 17 of the Crimes (Sentencing Procedures) Act says a penalty unit is $110, so the max fine is $2,200.
As you've apparently got a $500 fixed fine, there'll be legislation somewhere, probably in the regs under one of the transport acts, setting out fixed fines for various offences.