Chances are you've encountered a glitch that breaks the Thieves' Guild questline and will have to start a new game (since you don't have a previous save). You could try stealing something in plain sight (other than the ring) in the Riften marketplace, get caught by the guards, pay your fine and then see if Brynjolf's dialogue appears. You can also try the following (see below), but it is not a confirmed fix for this bug and may or may not work for you.
Brynjolf won't finish creating his distraction in the Market. The effect is that everyone will remain in the center of the market plaza, being told the "news" repeatedly and Brynjolf will not move, therefore not going to the Ragged Flagon to meet you for the next quest. This may be caused by planting the ring at night or speaking with Brynjolf before his distraction is finished.
- You may be able to solve this by forcibly pushing Brynjolf to the door of the Ratway. Then activate the door and quickly talk to him - he should then be inside the Ratway with you. If this does not work, reload and retry. Once inside, attack him, run to The Ragged Flagon and yield to him when you're at the bar. Talk to him quickly, before he can leave to go back to his stall, and you may be able to progress in the quest.