What's the address of your router? You need to enter this in the Dreambox communication setup as the Gateway Address or something. I guess the Dreambox's own address needs to be configured to match this address as well, e.g. if your router is 192.168.2.1 your Dreambox would need to be 192.168.2.n where n is anything but 1 (24 seems to be a common choice).
If the addresses seem to be OK, have you tried turning the router's internal firewall off for communications with the Dreambox address?
Triple Dragon, Dreambox 8000, Echostar AD3000ip, TBS6522,6925,6983 PCie cards. Gibertini 1.25m motorised dish driven by the AD3000, with either Inverto BU Quad or Norsat / XMW Ka LNBs . SMW 1.05m + 3 other dishes. Speccy: Promax HD Ranger+