If you backup first, you won't loose any data. Just copy the whole DB folder via FTP to your computer.
Next you can backup your settings, but this would be just for reference purpose. You copy folders config and templates.
Then install the QC PRO as a new installation, not reinstalling it into existing directories (mess could be result of that and if you're inexperienced, you would have to start over anyway).
From then on, I don't know the PRO version, so I cannot help. If there was any change in DB structure between free and pro versions, you can't just copy the db folder to a new pro installation, more changes are necessary. If you bought PRO version, ask the QC guys via e-mail for support.
If you are really desperate, perhaps I could help too, but that would be a paid service. If you get in trouble, let me know at http://www.nlp.sk/antispam/
