When you installed the program from the disk, the XML file from the trial version was still there with all of the program options, one of which was telling RootsMagic to open the last database used. So it did.
There is no problem because the file structure is still the same. If it was only a demonstration database, just use the File menu and Delete to get rid of it.
After you delete the demo database; close RootsMagic. Now click on your new database to open it the first time. After that using the RootsMagic icon will open what you want. This step is necessary to keep RM from getting lost on where the database you want is located.
Go to http://www.rootsmagic.com then click updates/rootsmagic This will allow you to download the latest version. It sounds like your antivirus is blocking you or you installed directly into the program folder in your C drive.