Players from Ukraine who are experiencing issues with ICQ.

There's another option for different browsers: use the friGate extension. With it, you can access social networks and various websites. If a specific website doesn't open, simply add it to the settings so that the proxy server is also enabled for it. After the blocking, I use it myself.

A browser version of ICQ with all your contacts (as Zawulon mentioned):
https://web.icq.com/
Log in, enter your phone number, confirm the code via SMS, and use it in the browser (and in the browser itself, install the necessary extension - friGate, Browsec, Zenmate, etc.).

You can also try the method described here:
http://forum.oszone.net/post-2738559.html

Or you can use programs like TouchVPN or VPN Master.
The Tor browser has no restrictions on websites.