If you have no access to cPanel from your home or office, log into your cable modem and see if these settings are enabled. If they are, then you have discovered the cause and will need to lower the blocking settings permanently or temporary when you need to connect to cPanel.
LAN-to-WAN: Allow as per below.
HTTP and HTTPS (TCP port 80, 443)
DNS (TCP/UDP port 53)
NTP (TCP port 119, 123)
email (TCP port 25, 110, 143, 465, 587, 993, 995)
VPN (GRE, UDP 500, TCP 1723)
iTunes (TCP port 3689)
WAN-to-LAN: Block all unrelated traffic and enable IDS.