What do I do if CPanel ports 2083 and 2087 do not work?

The stunnel binary listens on these ports and forwards the requests to cpsrvd (the web interface binary). Ensure that it is running.

root@cpdemo [~]# ps wwwaux grep stunnel
cpanel 25180 0.0 0.2 34572 1364 ? S 03:17 0:00 /usr/bin/stunnel-4.04local /usr/local/cpanel/etc/stunnel/mycabundle/stunnel.conf.run
root 31191 0.0 0.1 4764 672 pts/3 S 15:59 0:00 grep stunnel
root@cpdemo [~]#

If it is not running try starting it.

root@cpdemo [~]# ps wwwaux grep stunnel
root 31228 0.0 0.1 4764 672 pts/3 S 16:00 0:00 grep stunnel
root@cpdemo [~]# /usr/local/cpanel/startstunnel
root@cpdemo [~]# ps wwwaux grep stunnelcpanel 31241 0.0 0.3 3696 1656 ? S 16:00 0:00 /usr/bin/stunnel-4.04local /usr/local/cpanel/etc/stunnel/mycabundle/stunnel.conf.runroot 31243 0.0 0.1 4772 672 pts/3 S 16:00 0:00 grep stunnelroot@cpdemo [~]#