|Can you confirm that what you have given is the "exact" error message, if not let us know what it is.|
Have you an alternative browser (such as Firefox) onboard? If not it might be worth temporarily downloading one and installing it, which could prove a point.
If you have no other symptoms then its unlikely to be a virus but it would do no harm running your AV scans and maybe MalwareBytes frebie too (it can find what AV's miss).
There are two ways that a website can be blocked (although it usually displays "unable to connect"). These are Hosts files and IE Restricted Sites.
The quickest way to see if Hosts is involved is to temporarily disable it. To do so follow this path through your filing system:
You should see a file named hosts. Simply rename this to xhosts then reboot your computer and see if it helps. You can knock the x off later if it is not the culprit.
For IE Restricted Sites, from IE go to Tools > Internet Options > Security > Restricted Sites icon. Then use the button marked Sites. See if your banking site is on there. Easy if you are not using SpywareBlaster or SpyBot S&D Immunize. With the later onboard there will be a gigantic amount of blocked sites to wade through, although there are ways to temporarily remove their entries.
Please do not post then vanish - let us know the outcome