Uninstalling/reinstalling CCleaner won't help I'm afraid.
The 'trying to do something on the hard disk' message will just be a symptom of the issue.
I've not seen this one myself but in previous similar ones I have seen the software being updated wants something clicked or typed that CCleaner can't click/type or doesn't know to click. Something such as an extra UAC confirmation.
Which particular software update is it hanging on for you? (I assume that you have tried them one at once).