Hi Wehey and welcome,
This is one I prepared earlier !
I googled "blocking secure sites" and found at:-
http://answers.yahoo.com/question/index?qid=20091128204956AA3jPYlThe following underneath.
Kind regards,
Walter
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This smells badly.
Provided your browser has correct configurations (& it looks outwardly OK), I would say someone/thing is getting between you and the site.
Give this a shot for some analysis:
When on an SSL/TLS site, click the browser's padlock.
Carefully examine the pedigree of the certificate chain to see if there is any evidence of some unknown element in that chain, especially the final one.
I might just be there is a 'gateway' @ your complex, where the browser is getting the 'certificate' from, rather than the website itself.
This could mean the gateway is logging your encrypted traffic; then re-encrypting it before sending it on it's path to the destination server (bank).
If the gateway is not configured properly, these glitches could be the manifestation of that.
All mission critical connections over SSL should be verified with this padlock inspection of the certificate chain, before data is exchanged.
Added: It might be a matter of the 'negotiated encryption method' (maybe...).
Make sure you have your on board Certificates current; your time/date/time zone are accurate; make sure the browser has TLS & SSL (all versions) enabled.
Other than that I'm runnin' short of ideas.