No, it is impossible to become Jarl in Skyrim, unless you have a mod where you become Jarl of some town like Helgen which, to my knowledge, doesn't exist yet.
Skyrim Walkthrough Helgen Keep to Whiterun
Skyrim walkthrough begins with the hero or the prisoner being brought to Helgen Keep. This will guide the hero in starting up in Helgen Keep and then moving on to Riverwood and finally arriving at Whiterun to enlist the help of the Jarl (in the Imperial faction skyrim walkthrough). Skyrim is the most open ended rpg to date, and the side quests are as infinite as they come. This initial skyrim walkthrough will focus on the main objectives of the skyrim game, and also on the level up of the skyrim hero to suit the gamer’s playing style, be it destructive skyrim magic, stealth and sneak attack, vampire or werewolf specialization, bow and arrows ranged attacks or pure warrior melee combat.
Skyrim Begins in Helgen Keep with Unbound
In skyrim, the hero is brought into Helgen Keep as a prisoner, about to be executed for treason against the Empire. The prisoners, mostly stormcloak rebels, are brought before the Imperials and this is where character creation starts. There is a civil war between the rebels and the Imperials, and a third party is about to join the conflict to throw the whole civil war into total anarchy. Dragons.
Naturally, a dragon flies in and interrupts the otherwise smooth proceedings of the hero about to be executed on the chopping block. All hell breaks loose as the dragon tears through Helgen Keep. And Skyrim begins…….
In Skyrim, the hero must first survive the dragon in Helgen Keep in the Unbound Mission. Pick yourself up from the chaos all around, turn around and follow a man into a tower of Helgen Keep. Go up the stairs of the tower. The dragon will attempt to pick the hero off about midway through to the top and prevent the hero from reaching the top. Someone annoys the dragon with an arrow and it flies off again. The hero must now jump from this tower into the barracks below. Do that, and then go out of the barracks to face off with the dragon. At this point, the imperial guard Hadvar will lead the hero on to safety. A major decision of the skyrim game then occurs with the hero having to choose between the Imperials (by joining Hadvar) or the Stormcloak Rebels (by joining Ralof). This skyrim unbound mission will continue with the hero joining the imperial faction.
Skyrim Helgen Keep Dragon Attack
Skyrim Helgen Keep Dungeons and Caverns
In Skyrim, the hero follows Hadvar into the Helgen Keep Dungeons, where they are besieged by some stormcloak rebels. This initial part of the skyrim game is actually a tutorial for the hero in terms of interacting with the environment, with a particular emphasis on combat. The hero can wield an iron sword in his right arm and block with a shield in his left. Or use the magicka of Skyrim – wield the fire spell on the right and the Sparks electricity spell on the left. Or use Restorative magic on the left hand and an attack spell on the right. Either engage the enemies full on, or just sneak and stealth attack (these stealth attacks don’t work very well at the start of the game, due to the chaotic nature of the dragon attacks, and Hadvar by your side).
Descend further down into the dungeon and face off with more rebels. Here within Helgen Keep Dungeons, the hero can pick up a variety of low level armor and weapons. Also the hero is taught how to pick a lock. Remember to pick up the book on Dragonborns on the table. Now follow Hadvar and descend into the caverns beneath Helgen Keep.
One of the most exciting creatures to slew in the caverns beneath Helgen Keep are the giant spiders. Launch those fire spell attacks with the right hand and the spark electricty attacks with the left hand. Use Hadvar to tank the hero. Finish off the spiders and remember to pick up the spider frost venom and the spider eggs (taste one; they damage stamina, maybe an ingredient for a poison later?) Somewhere in the skyrim helgen keep caverns is the opportunity to sneak past some creatures, if the hero has not already learnt the art of sneaking and sneak attacks. Continue following the imperial guard until the hero reaches the outside and into Skyrim.
Skyrim Reaching Riverwood and Whiterun
In skyrim, Hadvar instructs the hero to follow him into Riverwood. Along the way, the hero can torch some black wolves with the fire spell if he so desires. Also the hero is brought to a shrine where he is asked to choose to touch one of three stones which will allow him to level up faster in magic, melee combat or steath techniques. At Riverwood, the hero speaks to Alvor the blacksmith for a brief understanding of what is happening in Skyrim at the moment. After this, stock up, and the hero is ready to embark on an open ended adventure of a lifetime. This includes the opportunity to play as a vampire in Skyrim.
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From Alvor’s house, head up the path to reach a bridge. Cross the bridge and follow the river north to Whiterun. Again more wolves will appear to attack the hero. This time, there is no Hadvar to tank the hero. Either use melee attacks or magic to destroy the wolves. The hero can sneak all the way to Whiterun to increase his sneaking skills. At a certain point along the way, the hero can catch a glimpse of a fort in the distance. This is Whiterun.
To reach the entrance of Whiterun, when facing the fortress before the river, turn left and run along some cottages until the hero reaches a bridge that takes him just before the gates of Whiterun. Speak to the guard and tell him that Riverwood needs the help of the Jarl. The gates will be opened and the hero enters Whiterun.