In general, googling your error message helps: have you seen this Web page, https://supportcenter.checkpoint.com/supportcenter/portal?eventSubmit_doGoviewsolutiondetails=&solutionid=sk30772?
Don't be fooled by the disclaimer that it concerns a discontinued product, the page was last updated on march 13th, 2014. Basically, it is a matter of traffic on port 443 being blocked.
As per your system admins claim that nothing changed on their side, did they really change nothing in OpenSSL? I find it hard to believe.