I need some help please..... pretty please even!

Hello all.
The other day I purchased a used laptop with the intentions of giving it to my son for a 13th birthday present. When I met with the seller everything seemed to be in order and looked good. I didn't try to go online with it, but it did show that it was connected to a network in the tray.
After getting it home I found quite a bit of personal stuff such as pictures still remained on the computer. I deleted all that and changed the pc name and the user name to my son's. Rebooted and went to connect to the internet. Then the problems began....
For starters, I have comcast cable internet that runs to a belkin router. 4 other computers, 4 phones, a wii, an xbox, and a blue ray player all connect with this same router.
Vista finds my wireless connection just fine and connects to it and says it has an excellent connection, but it won't let me change the name of the network from unidentified and if I change the network to private it reverts to public as soon as I reboot or restart the connection. Also, the computer will not access the internet. The status of the connection is shown as local access only.
I spent my whole weekend researching this, and found that it was a very common problem, but none of the solutions I found worked for me, I'm still right at the same place I was Friday night when I started messing with it.
Below is the copied text from ipconfig /all.

Microsoft Windows [Version 6.0.6002]
Copyright (c) 2006 Microsoft Corporation. All rights reserved.

C:\Windows\system32>ipconfig /all

Windows IP Configuration

Host Name . . . . . . . . . . . . : TRISTEN-PC
Primary Dns Suffix . . . . . . . :
Node Type . . . . . . . . . . . . : Hybrid
IP Routing Enabled. . . . . . . . : No
WINS Proxy Enabled. . . . . . . . : No
DNS Suffix Search List. . . . . . : Belkin

Wireless LAN adapter Wireless Network Connection:

Connection-specific DNS Suffix . : Belkin
Description . . . . . . . . . . . : Atheros AR5007EG Wireless Network Adapter

Physical Address. . . . . . . . . : 00-24-D2-B2-50-EE
DHCP Enabled. . . . . . . . . . . : Yes
Autoconfiguration Enabled . . . . : Yes
IPv4 Address. . . . . . . . . . . : 192.168.2.18(Preferred)
Subnet Mask . . . . . . . . . . . : 255.255.255.0
Lease Obtained. . . . . . . . . . : Sunday, July 19, 2015 11:49:39 PM
Lease Expires . . . . . . . . . . : Thursday, August 26, 2151 6:20:21 AM
Default Gateway . . . . . . . . . : 192.168.2.1
DHCP Server . . . . . . . . . . . : 192.168.2.1
DNS Servers . . . . . . . . . . . : 192.168.2.1
NetBIOS over Tcpip. . . . . . . . : Enabled

Ethernet adapter Local Area Connection:

Media State . . . . . . . . . . . : Media disconnected
Connection-specific DNS Suffix . :
Description . . . . . . . . . . . : Realtek RTL8102E Family PCI-E Fast Ethern
et NIC (NDIS 6.0)
Physical Address. . . . . . . . . : 00-1E-33-CF-E8-CF
DHCP Enabled. . . . . . . . . . . : Yes
Autoconfiguration Enabled . . . . : Yes

Tunnel adapter Local Area Connection* 6:

Media State . . . . . . . . . . . : Media disconnected
Connection-specific DNS Suffix . :
Description . . . . . . . . . . . : isatap.{001763C1-BDF8-4436-8237-6C0234405
D3D}
Physical Address. . . . . . . . . : 00-00-00-00-00-00-00-E0
DHCP Enabled. . . . . . . . . . . : No
Autoconfiguration Enabled . . . . : Yes

Tunnel adapter Local Area Connection* 7:

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

Tunnel adapter Local Area Connection* 11:

Media State . . . . . . . . . . . : Media disconnected
Connection-specific DNS Suffix . :
Description . . . . . . . . . . . : 6TO4 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 . . . . . . . . . . . : Teredo Tunneling Pseudo-Interface
Physical Address. . . . . . . . . : 02-00-54-55-4E-01
DHCP Enabled. . . . . . . . . . . : No
Autoconfiguration Enabled . . . . : Yes

C:\Windows\system32>

So there is all that for what it is worth. I tried manually configuring the servers after watching a youtube video about fixing the error, but Vista wouldn't let my primary and alternate DNS server numbers match, which they do according to what that person suggested.I'm pretty much completely stumped now.
In addition to these problems I noticed that the pc assigns a generic image icon to any picture that is stored on it, as opposed to a thumbnail of the image like I'm used to. Not an insurmountable problem, but not very convenient either.
Anyway, that is what I have going on. If you have anything you think I could try to fix any of these 3 things by all means please let me know.
Thank you very much for taking the time to read about my problems, and thanks in advance for any advice given.