Today, I decided to install Windows 7 as if my computer was new...
It was very good decision. It is the best way to check hardware functionality.
...I couldn't find the Toshiba Webcam application.
That’s somehow strange. When you open control panel > Programs and features you should be able to find it listed there. All preinstalled software are listed there.
I’m not 100% sure but this should start with Windows by default or you can start it manually using start > all programs > Toshiba > Utilities > Web Camera Application.
By the way: Is web camera listed in device manager under “Imaging devices”?