Can't connect to internet on a majority of things?

This is very frustrating because i'm trying to play some games with my friends but I can't connect to the internet. I can get online on my browser but I can't get online with some of my games. I can't connect to gameranger client or this other game client called voobly. I can't connect to online for some games on steam like call of duty world at war but I can connect to other games like counter strike. I also can't connect to minecraft online unless it's port forwarded. I can connect to anything though when I use a different internet connection, I usually am connected directly to my modem and when I use this connection all of this occurs, but when I use my wireless router none of this occurs but it has a much poorer signal. Ideally I wouldn't want to have to use the wireless router so please help me sort this out because it's very confusing and is making me angry.

Added (1). I just tried to do a ping test with the modem and then wireless router. With the modem connection it fails and says Packet Loss Test Error
Couldn't connect to the test server. A firewall could be blocking the connection or the server might be having some issues. Please try again later.
But with the wireless router connection it succeeds.

1. List your modem and router's make & model.
2. List the ping commands you've been using.
3. How many LAN ports on your 'modem'?