Q: MBP 13" Mid-2012 stuck on apple logo after installing Maverick

I own a MBP 13" Mid-2012 with Mountain Lion installed on it. When I upgrade to Maverick via Apple Store/Internet Recovery/USB it gets stuck on Apple Logo with a grey spinning wheel below. I tried disk repair with disk utility, and resetting PRAM but still nothing happens. When I reinstall Mountain Lion it works again. And no, unfortunately I don't have a back up. What to do? Please don't tell me to bring it to an Apple Store because all they have to say is that my logic board needs to be replaced which I couldn't afford. Help!