Many players are having issues with the group dungeon/LFR finder after the weekly reset, with various problems popping up, including not being able to queue at all.
Something broke with the reset (possibly related to the new LFR wing or timewalking), as player reports range from not seeing any dungeons or LFR options, to all raids showing up in the LFR selection (from Cataclysm onward), the find group button doing nothing, players receiving the “You are queued for too many instances” message for no reason, queues either instantly stopping or randomly stopping after a while, and even players getting removed from an instance after joining, snagging a deserter debuff as a little added bonus.
There are a few possible solutions with varying degrees of reported success, from joining or creating a pre-made group, to queuing up for a random battleground, but it seems this one will need an actual fix from Blizzard themselves.
You can keep trying your luck, as plenty of players reported it working after a while (and then not working later again).