ShortCircuited

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.