Deleting faces??

[micheus]

If I was unable to delete those faces, I would have selected them all and used the hole function. You can then closed up the open areaby selecting edges and using loop cut to create a new face to extrude from.

That's a good option.

A third option, similar this one except don't need holes (more easy situation). Select the edges surrounding the problematic area (an edge loop) and use Loop Cut. Or..., a fourth option, if it's complicated to get the region/edges selected right, in face mode, select all the "good" faces; Invert selection; Delete or Select Edge Loop Region to get the edge loop to use Loop Cut.