Open an empty map.
Check the data for blank entries (eg, long or lat missing a value)
Assuming that the coordinates are in decimal degrees and you specified longitude for X and Lat for Y and the sparial reference was defined correctly, add it to the map and check that the map is working alright with the data.
Use the Define Projection tool, if you don't get a chance to define it during the import step.
Save/copy the csv to a featureclass in a local file geodatabase.
Project it to your desired coordinate system using the Project Tool
Does it work now? or are you getting an error? and if so, hopefully the error is more than 999999
... sort of retired...