If you passed an online port test, there is a good chance the network error will go away when you get connected to a torrent.
My 6.x series BitTorrent will show a yellow status for a bit into a download.
My 5.x series does shows Online, ports open, pretty quick.
Which version of BitTorrent (Help>About) are you using?
A port in the 48152-65534 range is suggested, but that is only to avoid any possible conflict.
Check at Options>Preferences>Connection and make sure that the options Randomiaze port each time Bittorent starts and Enable UPnP port mapping are disabled.
I would suggest trying this torrent, KNOPPIX, before you change anything else.
It is almost always running fast and you should see good speed within a few minutes.
You don't have to download the whole file, although it is useful, just use it as a check of your down speed and connection.
