You may be able to figure that out by comparing profiles then.

• see also "This Connection is Untrusted" error message appears - What to do
  Secure connection failed and Firefox did not connect

I am sure you will be aware there are risks of using unsuported old Firefox builds. Security holes get fixed and the fixes are announced,

• https://www.mozilla.org//security/known-vulnerabilities/firefox/
• Do Not Install an older version of Firefox

Those using old versions may then be targeted by bad guys..

If you are with a secure private LAN that is fine, otherwise mitigation precautions include having well rehearsed bare metal recovery procedures, and/or using VMs.

Since you have a Kaspersky extension, I suggest checking the Kaspersky section of this article: How to troubleshoot security error codes on secure websites.

Why Firefox 39??

@John99 Non of those articles helped me. I'm aware of the risks.

@jscher2000 I followed kaspersky section of that article and disabled Scan encrypted connections and still get that error. Firefox 40 and up have scrolling lag. I tested Firefox 44 and this bug still was there (I'm not sure about Firefox 45+).

To better diagnose the certificate error, could you copy/paste the following to the address bar and press Enter to load it:

chrome://pippki/content/exceptionDialog.xul

On that tab, type or paste

https://openssl.org/

into the Location and try "Get Certificate". If that works, click the View button and compare the Issued by and Certificate Path sections with the attached. Any discrepancy?

Didn't worked

Could you inspect the certificate using one of your other (working) profiles? If there is a proxy or security filter operating, it should show up there too, assuming those are shared across all your profiles.

These pictures are from another profile. I'm not using proxy.

Could you check your TLS level setting:

(1) In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button promising to be careful.

(2) In the search box above the list, type or paste TLS and pause while the list is filtered

(3) If the security.tls.version.max preference is bolded and "user set" to some value other than 3, right-click it to restore the default value of 3

Do any other websites where you have problems connecting have more explanatory error messages?

Thanks. the problem fixed. security.tls.version.max was set to 1. other websites gave same error and now all of them opening.

Great.

For reference, max=1 means Firefox won't go higher than TLS1.0, while openssl.org only supports TLS1.1 and TLS1.2. It's very unfortunate that the error page doesn't come out and say that's the problem in the first place...