To find lines not connected on both ends, try:
1. Run Feature Vertices To Points tool (Data Management toolbox - Features) with the DANGLE option to get all dangle points. The output points carry ORIG_FID. Lines not connected on both ends will get two points.
2. Run Frequency tool (Analysis toolbox - Statistics) on the dangle points; specify ORIG_FID field.
3. Run Join Field tool (Data Management toolbox - Join) to join the lines/roads feature class with the Frequency table via OBJECTID and ORIG_FID; specify to transfer FREQUENCY field. Now any lines with FREQUENCY = 2 are orphaned.
Does that work for you?