The entrance to the southern car park is not visible nor obvious. It is not sign-posted. Station Parade is a direct route to / from the town centre.
It took me 30 seconds to find it on Google Maps. Carry on southbound over the bridge (passing the main station entrance), turn first left, first left again and you're there. Easy peasy! Car park appears to be accessible via Platform 1.
This is always a useful place to find the information you appear to require:
http://www.nationalrail.co.uk/stations/HAY/details.aspxThe trouble is most people know where the old and new entrances to the station are and it would not occur to them to take a few minutes detour down Nestles Avenue into the station car park, passing the driving test centre (where I failed then passed my driving test). Can you still access the station from the old entrance on the bridge? I didn't feel particularly safe waiting for a bus there at night in recent years and would walk on to Fairey Corner.