Problem with Safari 6.0.5. - can't open page....can't establish a secure connection... - after installing Mountain Lion 10.8.5.

I erased my MacBook pro mid 2009 and installed mountain lion OS X 10.8.5 - again I must say. I did all this before but Safari was acting up and I tried a lot of different settings but can't find the problem. So I erased everything again and did a re-install. Clean machine.. but still:

Now Safari (6.0.5) will not open pages: it will say "Safari can't open the page....because Safari can't establish a secure connection to the server......

Not for just a couple of websites but about 90 percent of the websites I try.

I need to run this machine in windows configuration for another program (only runs on windows :-( ) and I need internet access to different websites on both operating systems but for now mostly on the Mac side.. (I have deleted everything again, first want to get the MacBook working correctly).

I have played with DNS, IPv6, fire vault, firewall, etc but if you have suggestion...

Any suggestions please...?