Can't run anything; computer freezes up

Hello,
The past couple of days have been a pain. Yesterday when I tried to start my computer, it was really slow at starting up. When I finally got to the desktop, a popup came up that told me I needed to update Skype. I clicked no and then my computer froze up. I couldn't run any program's and eventually I just manually shut it down. When I restarted it, I clicked yes to updating Skype. After Skype updated everything worked fine. Today the same thing happened only its telling me to update adobe reader. The problem is that when I tell it to update, it says that it cannnot connect to my internet but everything is hooked up right. Can anyone help me out? I ran a hardware check and it said that my hardware was in bad condition and that I should backup everything but I can't do anything seeming how my computer wont let me do anything.