Problems accessing web sites in general can be the result of a number of things, but not being able to reach Microsoft and anti-virus sites is often the work of malicious infections.
I'm moving your post to our anti-spyware/anti-virus forum now; we'll help you out from there.
Once downloaded, follow these instructions to install and run the program:
Create a folder for HJT outside of any Temp/Temporary folders and move/extract HijackThis to that folder now. A folder such such as C:\HijackThis or C:\Spyware Tools\HijackThis will do.
Run HijackThis, but do not have HJT fix anything yet; only have it scan your system! Once the scan is complete, the "Scan" button will turn into an option to "Save log...".
Save the log in the folder you created for HijackThis; the saved file will be named "hijackthis.log". Open the log file with Windows Notepad, and cut-n-paste the entire contents of the Notepad file here.
The log contents will tell us a lot about what "nasties" have crept into your system, and once we analyse the log we can tell you what to do from there.