most likely its the game rather than your hardware. you did load optomized defaults when you got the pc? if not do so. making sure you enable high precision event timer, also called event timer or precision timer (ahci menu in bios if its there.) set your pci-e priority and boot order then save and quit.
run the game from a fresh start and after you escape on the way to the first village there is a mine. enter it. if the game crashes then its likely the game install.
my guess is you have a lot of unfinished or bugged quests. this will make your save file very unstable...
also check out the community patches at the skyrim nexus thye may fix your crash problem without you having to restart from fresh.