We introduced quite a few distractions to the solution of the puzzle, obfuscating the one key point without which the puzzle is unsolvable.
The opponent is within reach of your Mudbuttons if there were only a way to put both of them in the graveyard and have them deal their damage to the opponent (after attacking).
In short, the Hellbent mechanic on Keldon Megaliths must be activated to ping the second Mudbutton (first will be destroyed with your Fanatic). So the trick is to Thoughtseize yourself!
Eat the 2 damage, ignoring the Siphon-Mage’s tempting ability, and rid yourself of Damnation to empty your hand.
At this point, attacking would have done 3 damage, sacrificing Fanatic to kill one Mudbutton will do another 3 damage, and using Keldon on the second Mudbutton will deal the finishing blow.
Edit:
Thought it would be useful to outline opponent’s courses of actions to win should you pass the turn.
Case 1:
Your actions: Drain 2 with Siphon-Mage, and you attack with Mogg Fanatic, even if you don’t attack it won’t matter…
Life totals are now 6 and 5.
Opponents actions: Incinerate Mogg Fanatic. This is to prevent you from sacrificing Fanatic to kill the target of Oblivion Ring. Then Oblivion Ring one Mudbutton, and swing for the win.
Case 2:
Your actions: Thoughtseize opponent’s incinerate.
Life totals are now 9 and 1.
Opponent’s actions: Oblivion Ring Mudbutton. Attack with both Juggs, Taking 4 damage from the blocking Mudbutton and Fanatic.
Life totals are now 5 and 1.
Your actions: Regardless of your actions, you’ll still be in range for your opponent’s next Incinerate.
While Case 1 and 2 both work I think my Case 3 would be a better choice, since the opponent is tapped out. Since you didn’t specify who’s turn just ended I’m going with the tapped out person just finished.
Case 3:
When opponent declares end of turn, in response tap 2 mountains and the swamp to activate the mage ability and discard Thoughtseize and gain two life. Opponent: 7 Me: 5
Now it’s my turn:
Draw and play the swamp. Sac the Mogg Fanatic to do one damage to opponent to bring him down to 6. Cast Damnation to wipe all creatures from the board. This kills both Jugs and the torchrunners which sates their requirement and you do 6 damage to the opponent to bring him down to zero.
@Gohan: As with every magic gamestate puzzle ever written you start in your main phase, try again.
Case 2:
Your actions: Thoughtseize opponent’s incinerate.
Life totals are now 9 and 1.
Opponent’s actions: Oblivion Ring Mudbutton. Attack with both Juggs, Taking 4 damage from the blocking Mudbutton and Fanatic.
Life totals are now 5 and 1.
Drop the swamp, use the mage’s ability to get opponent to 3 and to get hellbent. Ping your ring’ed torchrunner and get the win?
Unfortunately Oblivion Ring removes the target from the game, so you cannot ping the torchrunner it targeted ;)