I'm using XP Home Edition Version 2002 Service Pack 3.
However, the problem mysteriously vanished when today I downloaded the full version of CCleaner from the site that you quoted. It installed as expected, and all now seems to work perfectly.
I don't think that the site you quoted is one of the two that I tried yesterday. However both the file that I downloaded today, and that which I downloaded yesterday (which didn't work) have the same size of 3,092 kb.
Since all appears to be well I have not tried installing the slim build.
Do you have any idea where the problem lay? I'm tempted to leave well alone now that the latest version of CCleaner works on my machine, but the symptoms I described do seem strange.