That’s not exactly what I asked, but I guess you’re not behind a physical router/firewall either…
Look in the console after clicking Play Online, if everything works correctly it will look something like this:
Requesting servers from the master...
CL_ServersResponsePacket
112 servers parsed (total 112)
CL_ServersResponsePacket
112 servers parsed (total 224)
CL_ServersResponsePacket
...
CL_ServersResponsePacket
112 servers parsed (total 3248)
CL_ServersResponsePacket
14 servers parsed (total 3262)
In your case there may be a clue to what goes wrong instead. Save it to file with /condump dump.txt and post the relevant parts her.