And most of the times I could see message "Performing TLS handshake..." in status bar, like it was stucked on something.
I have never found out, what caused this - if it was bug in newer version of Pale Moon, or some problem in my PC.
The strange thing was, that it only affected my home PC - and only Pale Moon. On my home laptop and on PC at work everything was working fine.
When I copied complete installation of Pale Moon (including all of my profile's folders) from work to home, it didn't help.
Today I tried to install fresh copy of Windows into Virtual Machine and then I installed latest Pale Moon - unfortunately the result was the same.
So I started to dig for solutions, unfortunately none of them worked. (for example set network.dns.disablePrefetch to true or set network.dns.disableIPv6 to true)
Until I found this topic:
Subject: Some HTTPS Sites Fail to Load (27.4.0)
and this post:
man, I really want to thank you very very muchasimperson wrote: ↑2017-07-28, 09:24Looks like if I use Pale Moon Commander to disable TLS 1.3 that gets the sites to work, but that's obviously not a desirable fix.

I installed that addon and started to play with those TLS settings until I found out that when I uncheck "ECDHE-RSA-AES-GCM 128 bit" in "Ciphers 1" tab, the websites started to work like a charm again, they are loaded immediately

so one more time, thank you
maybe this information will help somebody else in the future