Hi e_doug,
The download and installation of Indesign should not take more than a few minutes and it also depends on the network speed as well as the computer specs.
If the Creative Cloud Desktop App shows the apps as installed then please check your system, under Start > Programs, if you are able to find the application or not.
If not then please follow solution 2 and 3 of the KB : http://helpx.adobe.com/creative-cloud/kb/aam-lists-removed-apps-date.html
Regards,
Rave