So I had gone through the suggestion below already and allowed all of those and it didn't work. I had a Xbox 360 before and had nothing but problems so returned it to try the DSM-750 instead. In trying to set up the Xbox 360 they had me do the below and it didn't work, but it was already set when I installed the DSM-750.
But, the good news is I appeared to have fixed the problem, so all my time spent messing with the Xbox 360 isn't a complete waste. Mind you this has only worked for one night so far, so hopefully it will be a long term solution.
In case it helps anyone else, I wanted to post what I did. For Xbox 360 they had me open ports in Norton 360 (done by creating new rules with the specific ports) as well as opening ports on the DIR-655 in the virtual server.
For the DSM-750, in the FAQ there is a question that states: "How do I configure non-Microsoft Firewalls?" - in the answer a bunch of specific UDP and TCP ports are listed. I went through the virtual server for DIR-655 and opened each of those and in Norton 360 I created new traffic rules to allow each of those specific ports (you can use spaces between port numbers to have more then one port per rule).
For anyone who is not sure how to open ports. When I was dealing with the xbox 360, I just searched it for Norton 360 and found the answer online, and the d-link support people were helpful for the wireless router once I had the necessary port numbers in front of me.
I don't know that one or the other would have been sufficient, as I did both at the same time, and now that it is working, I don't want to mess with it.
Anyway, the end result is everything appears to be working for now.
Thank you ECF for your help.