IE 8 doesn't open certain website, firefox does

Checking the SSLLabs TLS protocol support (found at https://www.ssllabs.com/ssltest/analyze.html?d=brokerkf.ru), this site only supports TLS 1.1 and TLS 1.2. The most recent version of TLS that IE8 supports is TLS 1.0. So effectively, IE8 and the site cannot agree on a version of TLS to use, and as such your browser cannot connect to the site.

Note that this is also the case for every other user agent which gets that type of failure: all those products only support TLS 1.0 as the most recent version, while the server doesn't support anything older than 1.1.

It seems the site is not supporting older useragents, which can only use outdated TLS, see here: https://www.ssllabs.com/ssltest/analyze.html?d=brokerkf.ru
The result shows, that for a lot of older browser versions the connection is closed by the server. So this is not an issue with the pc you are using, it's done by the webserver itself.