My internet won't let me load some pages URGENT NEED PLEASE!?

Okay, I was trying to access some pages for my summer school assignment, and my computer went through one of those windows autmatic updates. I wasn't there to postpone it, so when i got back it had restarted itself. I went and logged in normally, and to my surprise it won't let me load some sites. These are sites I'd regularly visit. My online summer school class, a writing site, forums I post on, etc etc. They just won't load. It will load other pages like facebook, yahoo, etc. The internet browser tries to switch into compatibility mode, but it doesn't work. I switched over to google chrome which i have but never used and the same thing happened. Okay, I'm like something is REALLY wrong. There was no system restore point for me to go back to, and this problem is still happening while I am in safemode with networking. Now, I'm scared, and don't know what to do. This computer doesn't belong to me, its my grandmother's, and I'm using it to do my summer school which it won't let me get to. I need to know what's going wrong, because I'm on the verge of crying this second. I really need to know if something happened to the internet or my computer since my ipod is able to look at those pages fine. Please someone help me, soon. I don't know what to do; I'm seventeen and this is basically my grandmother's lifeline to her friends. Please, I need help!