Pinhead goes to Satan's fortress to either meet Satan and learn from him, or it find what knowledge he left behind (because the other demons aren't even sure if Satan is still alive, he sealed himself in his fortress thousands of years ago and hasn't been heard from since). What he discovered is that Satan committed suicide because he was so gay for God-senpai, that he couldn't bear to live without him. Pinhead goes on a rager, and mutilates Satan's corpse and then steals his sweet-ass golden armor that was hand-crafted by Yahweh himself
and wields mjolnirwears it and basically becomes Superman. The the other demons show up and are like "Yo Pinhead, get rekt, m8" and he was like "no u" and then went Pre-Crisis Superman on their asses and wiped out a couple of legions of the demon army, as well as the boss of hell. Then he's all like "Who runs Bartertown? Pinhead runs Bartertown!" d'Amour and his crew are just kinda chilling over in a corner, watching all this happen.
Then Satan wakes up, and he's PISSED!

Turns out he was only TEMPORARILY DEAD, as the LORD GOD ALMIGHTY has cursed him with immortality, so he'd be forced to forever live with his sins. After a few thousand years of studying dark majicks, Satan built this magical machine that would keep him in a permanent state of death as long as he was in the machine. But Pinhead busted the machine, so the spell was broken and Satan is alive again and not happy. At first Pinhead is like "Oh Satan-senpai, this is such a great privilege for you to have noticed me!" but Satan is all like "Yeah, and who the fuck are you? I'm tryin' get some damn peace and quite around here, and also why am I naked?" Pinhead decides that Satan is kind of a pussy and now that he's got the God Armor, he doesn't have to put up with this shit. So Satan and Pinhead go at it like Superman vs. Doomsday for a bit, until a battered Pinhead finally gains the upper hand and rips Satan to shreds.
d'Amour, still kinda chilling over in a corner is like "Okay, then. So. Is that it? We good? Can I go now? I got a thing" and Pinhead is like "Uh wait...hold up hold up. I...um...I got some other sights to show you, I swear it's gonna be sick, just don't leave yet." While he's momentarily distracted, the mangled corpse of Satan crawls up to him, and Pinhead's like "wtf breh, how are you even still alive?" and Satan's like "Immortality dude, I swear I just told you that not 2 minutes ago." and then pulls himself back together and pushes Pinhead's shit in and rips the God Armor off him. After seeing this, Henry is all "Okay, I'm leaving for real this time, deuces" and he peaces out and goes back to the Hell portal, which they figured out through some means that didn't even really seem to make sense to me , but I was beyond even caring at that point.
THEN! THEN! Oh you thought it was over, it's not over. Satan, I shit you not, just flat out punches a underwater dragon so hard that it crashes into the ceiling of Hell and shatters it, literally causing the sky to fall. You might think THAT was the end. Well, it's still not. While Satan was wilding out, Pinhead managed to escape alive, and he finds Henry and the old blind voodoo lady that Henry came to Hell to rescue and
HE RAPES HER TO DEATH. There's dick moves and then there's dick moves.

Then makes Henry blind, just for funsies.

EPILOGUE! Henry escapes from hell with his crew, blind and sans an alive old lady, and are deposited in the middle of Nevada. They try to hitchhike a ride (with the dead lady corpse) and are finally picked up by an evangelical preacher. And they're like "Hey, so why would you pick up a bunch of weirdos like us and a dead body, preacher man?" and he's like "So I could save your souls from eternal hellfire, you sad bunch of homos." and they're like "LOL, we just got back from Hell and that shit was wrecked, you're gonna have to get a new religion now haw haw, stupid evangelical!" and they all had a sensible chuckle while they kicked him out and stole his car. And then Marine Todd punched them (I wish) THE END.
Wait, EPILOGUE 2! Pinhead walks around Hell for a bit and then falls down some stairs and dies (not even exaggerating for lulz, this happened).