I don't have an excessive amount of software installed, no. I've not had any issues with earlier versions of CCleaner either. When I install an earlier version now, I get the same problem as above.
I should mention that each time I uninstalled CCleaner, I reinstalled from a brand new download, not the previous one I already had - I've done this four times!
When I boot in Safe Mode, the problem is still there - grayed out "Analyze" and "Clean" buttons, no list of applications.
I'm stumped...