What's wrong with my computer!!? Blue Screen, Unexpected Shutdowns, Websites coming up that arent suppose to..?

Ok, I am on my girlfriends computer. She has an HP Pavillion DV9000. Vista Premium on it. Yesterday she got the "Blue Screen of Death" So I tried to start it up multiple of times, wouldnt work. Then I decided to go into safe mode... Works fine, I ran McAfee Antivirus and F-Secure Online antivuris scanner. Found minor things & fixed them.. Didnt work. So I "TRIED" to download spybot search and destroy, some reason it wont dowload. then I tried to download spyware doctor wouldnt update which it said it needed to be able to update in order to work, I also ran registry mechanic, advanced system care, Spyware Terminator, Ad-Aware, CCcleaner, Auslogics Boostspeed and NOTHING has seemed to work. I restart the computer and it will let me start windows without safe mode, BUT with problems, Either my internet connection wont work, or it suddenly shuts down.. Sometimes i will restart and it will go on the logon screen then shut down again. Also when i say websites come up that arent suppose to, its not like they pop up.. If i type something in google it doesnt take me to the website I try to go to, it takes me to a bunch of other ones, but they stay in the same window... I see something under my all programs called DigitalHQ so I googled it and it seems to be a malware or whatever, I tried to remove the registry's still nothing. I deleted the program and nothing, I REALLY REALLY dont want to reformat it, That will be my LAST resort, so I would greatly appreciate any help you can give! Thanks!