ok. you can't just type your ipchicken address into the address bar of your browser. the only way that might work is if you were running a web server, but that's a different story.
so let me detail the 3 IPs you said you had.
- - one from IP Chicken: also called your "external" IP, this is the one that should show up on the dp serverlist, and thus anyone outside your house will use this one to connect to your server. this one will look similar to: nothing, really. the numbers seem pretty random.
- - "one from computer": if this is referring to your internal IP, this is the one that any other computers in your house would connect to. this will look similar to: 192.168.0.100
- - one from your dad: since you said it got you to your router, your dad isn't crazy after all. but all this is good for is changing your router's settings (for port forwarding and the like). this one will look similar to: 192.168.0.1
if your external IP changed, i'm GUESSING (somebody correct me if necessary) that the dp serverlist would automatically detect the new IP by the heartbeats sent from your server.
if your internal IP changed, your router might now be forwarding that port to the wrong place. the ideal thing to do would be to give your serving computer a static "internal" IP so that it wouldn't be a problem in the future. because otherwise, it would very likely be a problem.