Error establishing a database connection

I have big troubles. I wanted to transfer the mipc.org.au/wpmicp_2012 web to my server and went step by step trough the instructions. I made a backup the day before with the WP-DB Backup. I have also a backup from all files. Then I changed in Settings > General the WordPress Address (ULR) and Site Address (ULR) to the new Server. For a second Backup.
Somehow I got the message “Error establishing a database connection” Then I changed it quick back to the original one and saved the changes again. Now the message is still coming up. I can load the homepage, but the sidebar of the Suffusion theme is on the bottom and I can’t login anymore. If I open a page I get also the database connection error. I have several pluging installed, the most relevant are:
I have also installed the CaPa Protect plugin and login-with-ajax plugin
I tried to restore the backup but no success.
I tried to change the wpconfig but no success.
I’m at my end. I’m not very experienced with an MySql but I had a look at the tables and it’s pointing to the right place.
Theme: Suffusion 4.0.4
The web address is: https://www.mipc.org.au
WP is installed in the subfolder: /wpmipc_2012
Thank you for your help.