Well sorry this forum is pretty much dead, you cannot buy a new radio for this car but you can find ones that are rebuilt. There are only 2 radios that came with 84' models, the regular radio/stereo and the one that came with the leather/Digital package. There technically is a 3rd for anniversay edition. If you have leather/digi package you can ensure you get the right one.
You need to find someone that can remake these to be like new, these radios has a LOT of issues from the factory, I was on my 3rd unit replaced under warranty when it finally started to eat tapes in 95 and FM went in 96 so replaced with aftermarket setup (so much better). You can check around but Steve at 300zxpartsforyou.com may have one. I would call him
http://www.300zxpartsforyou.com/ and he can ensure you get the right parts.
There are also local shops that can rebuild stuff like this, but personally I would punt and just buy a new unit. My 84' has the best sounding stereo of any car that I own (including my S-Class Mercedes) the speakers and power were installed in 96' and I am on 2nd head unit (from Kenwood 6 disk changer, to Apline iPod controller which still works great) and with Kenwood speakers, 4x 600 watt power amp and 250 watt going to bazzoka tube (that is dating myself but it rocks).