This does seem to be a bit of a problem with Prados of this vintage, Steven. Sometimes the screen goes blank, other times the touch-screen won’t respond to input. Or, as in your case, the radio just doesn’t want to wake up when the ignition is turned on.
There are specialists out there who deal with these specific problems and seem to get really good results. Clearly, since the problem is a known one, some people have taken the time to conjure up a fix. There’s sure to be a specialist repairer near you in Queensland.