June,
There are so many ways in which a projection can be messed up in ArcGIS that
it is difficult to give you specific advice. But here are a few tips.
Close and reopen ArcMap after projecting, and reopen only the projected file
after. Check which coordinate system your map is in when you do the actual
projection, and see if it's different after you projected. If you start
from and netCDF, make sure to export it to raster and save the raster (do
not directly work on the raster view of a netCDF file). Once your raster
has been projected you can re-export it to netCDF.
Finally you might want to look into the NCDC THREDDS data server at
http://nomads.ncdc.noaa.gov:8085/thredds/catalog.html. They have NEXRAD
data available in a polar stereographic projection of a spherical Earth.
I'm not sure how they got from HRAP to that projected coordinate system, but
maybe you wouldn't have the same problem. Going from this PCS to your WGS84
GCS.
I'm unsure that answers your question but I hope that helps,
Cedric