Thanks Ian. Sorry for the late reply, but the disfunctioning "captcha" stopped me from replying ...
Where is your database stored?
> It is stored at the hosting provider. I use several other sql databases (wordpress and smf) at the same account. They work fine.
Did you setup the local installation to point to the remote database, or use a local database?
> the "mysql_TPH" is pointing to the remote database
> "PowerCMSConnection" is pointing to the local database
The error is basically telling you that it can't connect to your database using the root@localhost user.
> Yes, but where to look first to solve it? Do you have a "checklist" for determination...