Minecraft won’t start

Based on your description, you're using a different launcher than normal. Normal MC launchers don't have a "Force Clean" button. Try downloading the original launcher from here- https://minecraft.net/download

Click on the blue link that says "Minecraft.exe". Start it up and login, then in the bottom left it should say "Ready to download & install Minecraft 1.7.2".

Minecraft does not "install" like a usual program (in fact, Minecraft.exe is not an installer). When started, it creates and uses a folder for itself (.minecraft), which contains the *.jar executables and assets, but it doesn't create a new launcher executable that is registered in the OS somewhere.

Minecraft is launched through the Minecraft.exe file you originally downloaded (and is probably in a Downloads folder somewhere, or whatever you picked as the download directory), which then runs the .minecraft/launcher.jar archive in java.

I recommend moving (and, if necessary, downloading again) the Minecraft.exe to a "safe" directory (say, making a new Program Data/Mojang/Minecraft directory and placing it there, or moving it to the .minecraft directory itself) and then making a shortcut to it on the Desktop. Minecraft will not do this on its own, as I described above.