I'm genuinely not sure how your Edge has ever worked before but at least now I think we're making good progress.
Ports you require open are as follows:
External 25/TCP (SMTP)
Internal 25/TCP (SMTP)
Internal 50389/TCP (LDAP)
Internal 50636/TCP (LDAP)
Internal 3389/TCP (RDP)
3389 isn't really necessary but I personally like it open to be able to RDP into a server for remote support.
Internal, in this case relates to the firewall between your Edge servers and LAN (Assuming your Edge is in a DMZ).
Might I suggest that you look at that link I sent and just confirm that you've gone through the steps for everything?