Delete Face and Filled Surface capabilities

It looks to me like your surface may have other import errors causing problems.  Check out the small faces in the snapshots--this might have something to do with the surface Fill not working properly.

I suppose you could carve out these areas and redo them so the tiny surfaces aren't an issue--the geometry doesn't look terribly complicated.  I'd suspect the corner fillets are part of the problem with the imported surfaces, and the presence of small surfaces (like are shown in the snapshots) isn't terribly promising.

Good luck.

I managed to repair it, but as Jeff pointed out it does have other issues. I wouldn't want to try to tool this as it stands, if that is your intention.

Here's how I fixed it.

Original File

Deleted all features except "Surface-Imported1"

Right clicked on "Surface-Imported1" and ran "Import Diagnostics" and it found 18 faulty faces and 2 gaps between faces. Then clicked "Attempt to Heal All" it did a great job of turning it into a solid.