By "it is not the built in firewall" I assume that you mean you have confirmed it is completely turned off. If that is not the case, double-check to make sure that it hasn't reverted to being active because it used to default to on but the policies from the domain controller turnd it off during connection (which will not happen now as the domain controller isn't there).
Not seeing its DC should not otherwise affect incoming connections. You could try dropping it from the domain and using local auth (or joining the domain the other machines are on) to verify this makes no difference.
Also, check to make sure the machine has a correct IP address. It may no it it used to get its address assigned via DHCP from the old DC. Not having a correct address would stop it making outgoing connections to other machines on the subnet too though.