I've been trying different want to get into the game room. Personally, I don't have much problem with it, but here's some methods that I've tried/heard from others:
1) Close the tab and click "play online" again.
2) Click "play online" while signed out, and sign in through the game room tab.
3) If the game room tab directs you to the deck page, find your deck in the game room tab, and click "play online" in there.
4) Copy and paste the whole game room link. If it doesn't work the first time, copy and paste the second time. Here's the link: http://gaming.tradecardsonline.com/im/enterGamePlayRoom/game_id/76/deck_id/886254
Just change the last 6 digits with the deck id you want to use.
5) Click "play online", if it goes to the deck page, don't close the tab. Click "play online" again on the same deck from the original page.
I'll update here if I find any other solutions. And also do notify me if there are more ways. I'll add to the list.