Connection Problems When Doing More Than 1 Thing

I have had this problem for about a week now, ever since I returned after a week of vacation. For that week, the computer was off. Upon return, my dad had broken the router and I have to change my ip configuration from obtain automatically to giving it a specific one myself to fix the problem and return the router to its former operating state. I then returned the setting to its original form. The issue is now, I am the only one connected to my network, my resource monitor shows that only 2 things are using bandwidth of any relevance and those are the two things that I use on a regular basis, Teamspeak 3 and Counter Strike Global Offensive. When I first played CSGO after fixing the router, it was adequate alone, though I did notice that instead of a usual ping of 50ms it was closer to 80ms. Then, I joined teamspeak as I usually do and I was still fine, but the moment that I spoke a single word or even breathed into my microphone, my ping jumped to 1100ms and stayed there until I stopped using my microphone. After trying anything I could myself to get it working again (A full list of things that I have tried is provided below) I tried my ISP and was told by them that the router's connection to them is very strong, and that they see no issue with other computers. I tried the exact same setup on my laptop, and sure enough, it worked fine. The problem is, if I do more than one thing, so CSGO and try to use Skype, Teamspeak or ingame voice, I spike to 1100ms on all of them.

Additional Info
I have 2 ethernet adapters in the computer, 1 in the motherboard and one as an expansion, both presenting the same issue.
I am connected by Ethernet to the router.
My ping while speaking in teamspeak and playing CSGO is usually under 60ms.
From what I can tell, the problem seems to be in the upload traffic because I can hear others fine without having any additional latency problems.
I do have a basic knowledge of technology.
This Problem is found ONLY in this computer.

Specs (From DXDIAG)
Operating System: Windows 7 Home Premium 64-bit (6.1, Build 7601) Service Pack 1 (7601.win7sp1_gdr.150316-1654)
Language: English (Regional Setting: English)
System Manufacturer: To Be Filled By O.E.M.
System Model: To Be Filled By O.E.M.
Processor: AMD FX(tm)-6300 Six-Core Processor (6 CPUs), ~3.5GHz
Memory: 8192MB RAM
Available OS Memory: 8148MB RAM
Page File: 5587MB used, 10707MB available
Windows Dir: C:\Windows
DirectX Version: DirectX 11
DX Setup Parameters: Not found
User DPI Setting: 96 DPI (100 percent)
System DPI Setting: 96 DPI (100 percent)
DWM DPI Scaling: Disabled
DxDiag Version: 6.01.7601.17514 32bit Unicode
Gigabit PCI express Network Adapter

Regular Ping
50-60ms

Ping Now
80-100ms

Ping When Using Teamspeak Now
100-1750ms

Things I Have Already Tried
Direct Connection computer to Modem
Updating Device Drivers
Rebooting Computer
Rebooting Router
Contacting ISP - They told me I most likely have an internal issue
Contacting Geek Squad - They tried to sell me thing
Re-configuring My Network Adapter
Rebooting My Network Adapter
Changing My Ethernet Cord
Changing My Network Card
Using Resource Monitor to Find any Secret Network Users
Command Prompt "ipconfig" changes (release, renew, flushdns)

I hope that I can find some help here.
Thanks in advance

-Bo :)