compund path background

You could try and use Live paint. 

But first make a copy.

Then go to Object > LIve Paint > Gap options and set the gap detection to a high values.

Then take the live paint tool and click inside the gaps. Does that work?

The other option would be to do Object > Path > Offset path.

Offset it so much that all the gaps are closed.

It will make a copy automatically.

The copy is selected afterwards

Then in the pathfinder panel hit Unite (top left)

Then use Offset path again, this time using a negative value.