When the mldonkey package in debian/ubuntu does not work properly you may very well end up without any error messages in all log files. When you try to login as user mldonkey to start it manually, that won't work either, because it doesn't have a shell. So what to do?
It's actually quite straight forward: You supply a shell manually when changing to user mldonkey: sudo su mldonkey -s /bin/bash
Then you simply cd ~; mlnet
And it should print out some error message. For me it complained about downloads.ini.tmp being in the directory and exited.