Spoilerized for people who don't want to know:
The game starts with the Prof. selling PE to Mom. She now owns 51% of the Earth and makes herself it's evil overlord. The PE crew decide seeing as the Earth is no longer safe, it's time to go elsewhere. But unfortunatly, the PE Ship is all whanged up. They're able to fix everything but the dark matter engine. Farnsworth pawned the backup engine to get a gun, so it's up to Fry to sneak through the sewers and behind the cover of Mom's wandering Death Trooper robots to retrive it.
Once that's done, the crew escapes, only to find that Mom's after the Professor. See, Mom's turned the Earth into a giant warship so she can take over the universe, but the only person who knows how to make an engine powerful enough to move the Earth is the Professor. She locks the PE ship in her tracktor beam of some desolate planet, and t's up to Bender, who abandoned ship, to save them.
He does, but neglets to disable Mom's ship. Mom and her sons kidnap the professor and behead him, keeping his head in a jar to power the Earth's engine. Mom also sends the ship heading straight into the nearest sun, where they promptly run out of dark matter fuel. They strike a deal with the natives on the sun to defeat the dark God who has taken over their world (who turns out to be just your normal, omnipotent, all-knowing deity) in exchange for some fuel. After Leela kicks his butt, they head to the Bogad system to visit the professors old mentor Adoy, the only one who can help them. He has a time machine, but it's up to Dr. Zoidberg (making a cameo) to power up it's generator. That done, the PE crew rocket back in time to PE ealiy that morning, create a time paradox by replacing their whanged-up version of the ship with the fresh one there, and race to Mom's to stop the Professor from selling PE. But will they make it?
That said, shouldn't this be in the Stockroom board?