Simon Petrikov used to be an archeologist/anthropology enthusiast. He found a strange crown that deteriorated his sanity, gave him intense hallucinations (well...they're not really hallucinations, but other humans can't see them), and changed his physical appearance. The crown also gave him ice-related powers whenever he wore it. During this time, a nuclear war broke out (known as "The Great Mushroom War"), and a nuclear winter soon followed. Simon was able to survive the winter because of the crown's powers. He fought against the crown's influence, however, to keep his sanity. Some indeterminate time afterward, Simon, searching the wastes, found a small demon girl named Marceline and began to travel with her/protect her. She pretty much gave him a reason to live. However, Simon soon found that it was necessary to use the ice powers granted by wearing the crown to protect Marceline and himself from the post-apocalyptic creatures that littered the wastes. As such, his sanity gradually began to wither away, and he always scared Marceline whenever he would put on the crown and become the "Ice King". Marceline noted that he was getting worse, and the insanity started to happen even when Simon didn't have the crown on. As such, Simon promised Marceline that he would never put on the crown again. The pair traveled the wastes, and Simon acted as a father figure to Marceline, giving her life lessons and cheering her up through jokes and badly-acted Cheers renditions. Not long afterward, Simon noticed that Marceline had a fever, so he scoured the city they were in for "chicken soup" to heal her (it's implied that Marceline didn't have a fever at all, Simon's hands were just becoming colder and colder). Simon found a food truck, but kicked it off the bridge it was on in anger, when he discovered it only held clams. The truck let off a siren when it hit the ground, and attracted a shitload of mutants, who chased Simon and Marceline, cornering them in an alley. Marceline knew they were both going to die. Simon said "not yet", and hid Marceline in an abandoned car. Facing the mutants, Simon took out the crown and told himself that he "has to keep it together. For her." [url=http://www.youtube.com/watch?v=o1-GMVVrtAg]Desperately trying to retain his grip on reality, Simon begins singing the "Cheers" theme and puts on the crown.[/url] He's able to knock off the crown after defeating the mutants, and he returns to Marceline. She tells Simon she loves him, and he responds with "I love you, too, Gunther", clearly indicating that his mind isn't completely his, and will soon be fully lost. Eventually, Simon fully becomes the Ice King, and completely forgets himself and Marceline. Marceline, grown-up, avoids him as much as she can, ashamed of seeing her former father figure in such a state of delirium.

I still think that Finn is actually in a hospital bed, forever in a coma.

There really isn't a legitimate storyline. It's just the random adventures of a kid and his dog. If you're talking about the back story, well then I have no idea.