Gmod Multiplayer doesn't work in my Local Network?

Problem has been resolved!
So Gmod multiplayer refuses to work under any circumstances on this laptop… or so I thought.
Let me explain. Ever since New Year’s Day 2014, multiplayer in this network has been disfunctional for every PC. Why? None of us know. When we try to connect to any server, the access is denied.
Just recently, though, I went over to a buddy’s house, taking my laptop with me. Once I got there, I explained to my friend the problem (problem explained better here). I was hoping he could help me since I have done every blasted solution I could scourge up online with no success.
I booted up my laptop, connected to the house’s WiFi, and started Gmod.
Multiplayer was working for the first time it had in months!
I tried to explain to my buddy that, at home, it hadn’t been working for so long, but he passed it off as me being insane. I had the idea in my head, though, that multiplayer might be working yet again!
Excited, the first thing I did when I got home was boot up Gmod and have a good time online.
Multiplayer was broken. Again.
Utter disappointment washed over me.
Why is this? Why does it work in his WiFi and not mine?

Does it work to play other Steam games in multiplayer such as the Counter Strike, Team Fortress or Half Life series?
If not, I believe someone has configured your router to block such traffic. Since it works to play the game at your friends house, your firewall is correctly configured. My best guess would be someone in your family configured your router to block such traffic or your ISP is blocking it. Although I can’t understand why your ISP would do so, but try call them and see if they can help you. Confront your parents and siblings first though.

If the other games work, and you did what code_gs suggested in the other thread, something is definitely wrong and I’ll have to do some research in order to help you.

I’ll await your answer.

All, and I mean ALL of my other games (Steam and non-Steam) have working Multiplayer.
I’ll go ahead and check the router and firewall…
Question though, what is the ISP?

Internet Service Provider - The company that delivers your internet. Comcast, AT&T, etc.

Sorry for the late responses.
I have been able to conclude that it is probably a problem with our ISP, or our modem is just being stupid.
We have tried everything at this point, going so far as disabling Trend Micro, Windows Firewall, and opening our router to outside attacks for a short time. None of these work.
I’m just going to leach off of my friend’s WiFi every time I wanna play Gmod. Since he lives close by, its no big deal.

And now we even tried resetting the router.

i think its your computers firewall that have blocked all gmod connections. So try to unblock gmod.

I’ve recently been thinking about dishing out some of my budget for a new router, with about 3 times as much internet speed.
Would this potentially fix the problem as well?

I doubt that it would.

Switching from Time Warner internet to Verizon this Friday. New modem, new router.
This isn’t just for Gmod by the way, it was about time to upgrade anyways.

Forgot to mention this a long time ago when I finally got the new modem, but it works now.
Problem solved!