Sounds like your ISP has issues. You can connect to certain websites, but not to others? That sounds like DNS issues.
Try these simple tests.
Start,
Run,
CMD to open a command prompt:
PING 64.233.161.103
PING
www.google.com.au
Right click in the command window and choose
Select All, then hit
Enter.
Paste the results in a message here.
If you are on a machine with no network connection, use a floppy, USB disk, or a CD-RW disk to transfer a text file with the information to allow pasting it here.