Make sure you go there as a Adult, as biggoron is not there as a child.

think i may know the problem.

rule is you have to run (using epona of course) all the way there.

do NOT teleport to the fire temple and go out from there. it wont work. as someone said a cutscene will occur when you get there.

Did you buy a biggoron sword and then it broke? Or are you doing the trading process ( Don't let this question confuse you if the first question is what happened ) ?

He is at the other side of a kind of mountain wall... It took me a while to notice him, just wander around beside the Death Mountain Crater for 2 minutes or so and you'll find him sooner or later.

As adult Link, go up to the peak of death mountain. If you climbed your way there then once you come up and you're facing the crater and fairy caves, biggoron will be on the right side just behind a small wall. Walk up to that wall and biggoron will come up.

As an Adult, you must have beaten Volvagia. you must have also gotten the broken sword from the Carpenter Boss in Gerudo Valley via the trading quest. because the broken sword does not have a time limit attached to it, you CAN warp to the crater using the Bolero of Fire song. Hookshot toward the Goron city entrance, but take a left toward the Magic Fairy cave. Jump across the gap and climb up the ladder to the first part of the crater and exit onto Death mountain's peak. from here, run to the left side of the peak and the Biggoron will wake up. this allowing you to continue your trading quest.

You can complete the whole Biggeron trading quest as soon as you obtain Epona.. Don't attempt this quest without Epona, as no matter how much rolling you do, you'll never make it within the time limit.

I kinda think you have the broken sword you broke and not the one you traded for.

really, my brother couldnt find him either and I laughed at him

I think this question is funny

At the summit, go all the way into the nook on the right. At first it doesn't look like he's there, but he is.