Welcome to the world of Dell.
The one and only Dell i ever had broke 3 times in less then 6 months, i canceled all the warranty's thy gave me more money back then thy where supposed to, but then i called in a year later to get it repaired for the heck of it and it shows by them that im still under warranty which then the computer was fixed 2 times since and is no in the garbage already, s there might be a chance that you can get the mother board fixed with out paying, you just gotta give it a try.
But the best thing is to switch to a father board and get a Mac.