Intersect (analysis) of polygons generating empty output

Follow these steps:

1. Visually verify that the polygons do indeed intersect using Arcmap
2. Restart Arcmap
3. Ensure that features are not selected
4. Re-run the intersect

I was experiencing very similar difficulties, and tried repairing geometry with all files to no avail. What eventually worked was placing both files into their own file geodatabase, and then running the operation.