Safari, on the blink.
Hello, ..
I'm currently, for some reason, new to me, unable to connect to any sites on the net, using Safari v. 5.1.1.
iMac, Mac OS X (10.6.8)
It's because your Mac is running v10.6.8 Snow Leopard. It's such an outdated OS X, you're bound to have problems with Safari.
Try using the Firefox browser instead > https://www.mozilla.org/en-US/firefox/new/
See if your Mac can upgrade to v10.11 El Capitan > Upgrade to OS X El Capitan - Apple Support
That way you would have Safari 9.1.1 installed. The latest version for Safari available.