If you have installed Radiant correctly, Radiant will ask you where your quake3.exe is installed. There should be sample maps inside your working directory of your Quake III installation than (q3dm1sample.map. q3dm7sample, etc.) You can try to compile those and see if everything will work as intended.
Make sure no entity is outside the world (void) or inside brushes.
Make sure you really have the created AAS file in the correct directory when loaded into game, coupled with the matching bsp file. If you are not sure, put foo.bsp and foo.aas into a foo.pk3, inside your baseq3 directory.