I downloaded some Stardock applications and now I want to uninstall it because its kind of heavy on my system. I tried to go to the start button on the bottom left and find the application and click to uninstall it. It saids that it couldn't find the INSTALL.LOG, so I went to Control Panel to try and uninstall it, it didn't work either.

Next, I tried going to Program files and find the app's INSTALL.LOG myself, but when I looked in the application's folder, I couldn't find INSTALL.LOG anywhere! What do I do?

This will happens sometimes, when installing a program, the installation will make this log file and put it somewhere in case you want to uninstall

At this point the uninstall program cannot find the file where it was put when installed

What you can do is
-boot into safe mode and delete the folder that you installed stardock to

-reboot in normal mode and download this
Windows Installer Cleanup
Download windows installer cleanup, open app and go down list till you see stardock and highlight then click remove, this will remove any installer info left behind by programs removed from system.
http://download.microsoft.com/download/e/9/d/e9d80355-7ab4-45b8-80e8-983a48d5e1bd/msicuu2.exe

-Now download and run this

ccleaner (Freeware)
Download CCleaner 2.16.830 - FileHippo.com (http://www.filehippo.com/download_ccleaner/)
On the right hand side, click download latest version

At this point, stardock should be removed and invalid settings in registry should be removed by using ccleaner