Internet keeps going out: Default Gateway and DNS Server error

I am running Windows 7 64-bit. My Internet connection keeps getting dropped, and when I run the troubleshooter, I can get two different messages: "(DNS server) is not responding" or "The default gateway is not available." When I get the former, I have to restart my router. Any amount of time later, my connection is dropped again. It can be a day or just a couple of minutes.

I'm using an Arris DG860A provided by time warner cable. Seems to drop more frequently when i run a P2P program. I also thought about upgrading my Realtek PCIe GBE Family Controller from version 7.50.1123.2011 to version 7.073.0723.2013

Here is my ipconfig /all:

Windows IP Configuration

Host Name . . . . . . . . . . . . : Richard
Primary Dns Suffix . . . . . . . :
Node Type . . . . . . . . . . . . : Hybrid
IP Routing Enabled. . . . . . . . : No
WINS Proxy Enabled. . . . . . . . : No
DNS Suffix Search List. . . . . . : socal.rr.com

Ethernet adapter Bluetooth Network Connection:

Media State . . . . . . . . . . . : Media disconnected
Connection-specific DNS Suffix . :
Description . . . . . . . . . . . : Bluetooth Device (Personal Area Network)
Physical Address. . . . . . . . . : E0-06-E6-31-0A-90
DHCP Enabled. . . . . . . . . . . : Yes
Autoconfiguration Enabled . . . . : Yes

Ethernet adapter Local Area Connection:

Connection-specific DNS Suffix . : socal.rr.com
Description . . . . . . . . . . . : Realtek PCIe GBE Family Controller
Physical Address. . . . . . . . . : D4-BE-D9-A5-D0-D7
DHCP Enabled. . . . . . . . . . . : Yes
Autoconfiguration Enabled . . . . : Yes
IPv6 Address. . . . . . . . . . . : 2605:e000:9d00:2500:212b:715b:4f59:abbf(P
referred)
Temporary IPv6 Address. . . . . . : 2605:e000:9d00:2500:a0c5:4b07:455e:6091(P
referred)
Link-local IPv6 Address . . . . . : fe80::212b:715b:4f59:abbf%11(Preferred)
IPv4 Address. . . . . . . . . . . : 192.168.0.3(Preferred)
Subnet Mask . . . . . . . . . . . : 255.255.255.0
Lease Obtained. . . . . . . . . . : Tuesday, September 10, 2013 9:47:17 PM
Lease Expires . . . . . . . . . . : Tuesday, September 10, 2013 10:47:46 PM
Default Gateway . . . . . . . . . : fe80::21d:d4ff:fe9b:4591%11
192.168.0.1
DHCP Server . . . . . . . . . . . : 192.168.0.1
DHCPv6 IAID . . . . . . . . . . . : 248823513
DHCPv6 Client DUID. . . . . . . . : 00-01-00-01-17-50-EF-F8-D4-BE-D9-A5-D0-D7

DNS Servers . . . . . . . . . . . : 209.18.47.61
209.18.47.62
NetBIOS over Tcpip. . . . . . . . : Enabled

Tunnel adapter isatap.{DDB4FF5E-213D-433D-918D-99B96DEC80C8}:

Media State . . . . . . . . . . . : Media disconnected
Connection-specific DNS Suffix . :
Description . . . . . . . . . . . : Microsoft ISATAP Adapter
Physical Address. . . . . . . . . : 00-00-00-00-00-00-00-E0
DHCP Enabled. . . . . . . . . . . : No
Autoconfiguration Enabled . . . . : Yes

Tunnel adapter Local Area Connection* 12:

Media State . . . . . . . . . . . : Media disconnected
Connection-specific DNS Suffix . :
Description . . . . . . . . . . . : Microsoft 6to4 Adapter
Physical Address. . . . . . . . . : 00-00-00-00-00-00-00-E0
DHCP Enabled. . . . . . . . . . . : No
Autoconfiguration Enabled . . . . : Yes

Tunnel adapter isatap.socal.rr.com:

Media State . . . . . . . . . . . : Media disconnected
Connection-specific DNS Suffix . : socal.rr.com
Description . . . . . . . . . . . : Microsoft ISATAP Adapter #2
Physical Address. . . . . . . . . : 00-00-00-00-00-00-00-E0
DHCP Enabled. . . . . . . . . . . : No
Autoconfiguration Enabled . . . . : Yes

Tunnel adapter Teredo Tunneling Pseudo-Interface:

Connection-specific DNS Suffix . :
Description . . . . . . . . . . . : Teredo Tunneling Pseudo-Interface
Physical Address. . . . . . . . . : 00-00-00-00-00-00-00-E0
DHCP Enabled. . . . . . . . . . . : No
Autoconfiguration Enabled . . . . : Yes
IPv6 Address. . . . . . . . . . . : 2001:0:9d38:6abd:b0:21d7:3f57:fffc(Prefer
red)
Link-local IPv6 Address . . . . . : fe80::b0:21d7:3f57:fffc%16(Preferred)
Default Gateway . . . . . . . . . :
NetBIOS over Tcpip. . . . . . . . : Disabled

Speed Test:

Speedtest.net by Ookla - My Results

https://www.speedtest.net/result/2960753486.png

My roommate and I both stream video frequently on Netflix and Youtube. I'm the only one who uses P2P and when I game I shut everything else down usually.