Apparently most links work when you click on them? Are you using a HOSTS file which stops "bad" sites from loading. If so, then you may need to alter the HOSTS file so those sites will open.
What types of sites are these? Can you list some of them?
You also need to make sure that Internet Explorer security options are set to "medium". While in Internet Explorer, click on "Tools" in the upper left, choose "Internet Options". When that loads, click on the "Security" tab, then click on the "Internet" icon (the world globe), then click on the "Default Level" button. That should set the security settings to "medium".
If that doesn't get it done, try installing the most recent version of Sun's Java from the link below:
After clicking on the link above, click on the "Download J2SE JRE " link in the "J2SE v 1.4.2_05 JRE includes the JVM technology" section to start. At the next page, accept the license agreement, then choose the "Windows Offline installation" to download the full installer to your desktop. Once it's there, scan it for viruses, just to be sure, then shut down all background programs including your antivirus, then double click the file to install it.
Hope this helps.