That should work. What was the result? You need to be operating in the proper editing context. Is the tower a group or component? If so, you need to open the group for editing (e.g., double-click on the tower when the Select tool is active) before you can make any changes, such as running Intersect With.
If you can, I suggest uploading the SKP model file here so that other users can suggest more targeted ideas.
Your cylinder is a group and the intersecting geometry is loose and outside of the group. Explode the group so the cylinder geometry merges with the rest.
Keep in mind that as it is, it won’t be 3D printable. The cylinder wall has no thickness. I don’t know what you want from here but it’s probable there’s a different and better way to get to what you want.