Hi,
if your ISP has to use a CGN due to lack of global IPv4 addresses (as a result of IPv4 address exhaustion) he usually deploys addresses from within the so called "Shared Address Space" to the WAN interfaces of his customers' CPEs (your DIR router). This is the address space 100.64.0.0/10 which is the short form for the range 100.64.0.0 - 100.127.255.255. Any ISP who is forced to use a CGN can use this address space, hence it isn't unique and cannot be routed within the Internet, similar to private addresses like 192.168.0.0/16 or 10.0.0.0/8. For details see
RFC6424,
RFC6269 and
RFC6598.
ISPs who use CGN for IPv4 Internet access usually also provide IPv6 Internet access (e.g. DS-Lite), hence you could reach desired ports on your "static IP machine" via IPv6 from the Internet, given your DIR device also supports IPv6 and you get a fixed IPv6 address range for use inside your LAN (otherwise you would have to use some DynDNS solution).
Of course IPv6 is not yet widespread and commonly used by Internet users, hence nowadays reachability via IPv6 is of limited use only.
If you want your 'static IP machine' to be reached via IPv4 from the Internet, you would have to use some VPN service provider. You would install a VPN client software (e.g. OpenVPN) on your static IP machine and connect to the VPN ISP. He would use a public IP address either for provision to your site's internal tunnel endpoint or for use at his site to NAT and forward traffic through the tunnel to a private IPv4 address assigned to your site's internal tunnel endpoint. Of course this service is probably not for free, hence it could be more advantageous to change to an ISP who offers a real public IPv4 address to your router.
PT