mysql_query error after PHP upgrade

My host upgraded to PHP 5.5 today, so parts of my site have stopped working ??

I get errors like this one in a few places:

mysql_query(): Access denied for user ‘root’@’pro20.meebox.net’ (using password: NO)

Most of my site is working, the error is only found in my child theme + two plugins.

Any idea how I can fix that?

Thanks,
Mads