My server has no Mods on it all, as I haven't worked out how to do that yet.

Update to this - I have discovered that I also cannot log on to Whitelisted servers too it seems! I set my own server up to use Whitelist, and put my 44 char GUID in the relevant whitelist.txt, but the game tells me that I am not Whitelisted for the server. Remove the Whitelist (and no password) and I can log straight on to it.

Tried that, but with no difference. Afterwards, I tried putting one of the passworded servers in the Parameters section of the Launcher, but that didn't work either and so I removed it.

Yes, doing it that way the game just seems to hang.