HI erdi65 
The uninstaller, will Uninstall the program files which it installed,.
It won’t “uninstall” files created after installation, such as your Preferences, and serial number activation, and obviously any shaders/objects/scenes etc.. which you’ve created.
The preferences file is stores in Users/(your name)/AppData /Roaming/Daz3D/Carrara
I’m not certain where the serial number is stored, probably in Regedit somewhere, ...but it shouldn’t stop you either removing Carrara, or adding Carrara again, ..or adding a different version of carrara.
With or Without a serial number, Carrara should install and open.
You can then register a serial number, or change the serial number by going to the little Daz Logo at the top left corner of the main screen in Carrara, and clicking on the option to Register Carrara.
I have made a clean Install and after that, Carrara asked me not for my serial number.
Carrara fails to start, no Error Message, nothing.
Q: Are you running the program as Administrator. ?
You need to do this to save the serial info.
But,.. as far as i know, it should still run carrara, although it will not have saved the serial if you’re not admin.
Hope it helps 