Your question, such as it is, does not provide much to go on other than seeing the words "Unidentifed network" twice in bold letters, what exactly is the problem.
Unidentified network might suggest that you are not receiving DHCP information from something (unknown) providing DHCP resolution for your network nodes. So maybe you could start, by telling us a little bit more about the issue and filling out your system specs in your member profile. Some specifics on the manufacturer model name model number and version number of your network adapter as well as any router or other device between the problem PC and the internet might help. Wired connection, wireless connection, both, either?
In the mean time perhaps just manually assigning static entries for the IP addressing scheme for the adapter may get you over the hump, I know you said you've tried this but what type of addressing scheme did you use, and when you did try it, how much did you test, just because you weren't able to connect to the internet doesn't necessarily mean you didn't have a network connection. Did you try to ping other hosts or the router's inside edge. Can you provide a screen shot of an ipconfig /all from the command prompt. Also if the machine has multiple network adapters, please disable the one(s) you are not using.
You've mentioned that you've "tried new drivers"
Yesterday was, Today is, but ahh Tomorrow...mystery, suspense and a promise of hope.

Operating System Windows 7 Ultimate 64 bit
Computer Type Home built
OS Service Pack Service Pack 1
Internet Explorer Version IE9
DirectX Version 11
CPU Type and Speed AMD Phenom II X6 1090T Black Edition Thuban 3.2GHz
CPU Cooling Stock Factory Cooler
CPU Idle Temp 32C
Motherboard Chipset GIGABYTE GA-870A-UD3 AM3 AMD 870
System BIOS Revision Award F5a (beta) 11/15/2010
System Memory Type G.SKILL Ripjaws Series 16GB (4 x 4GB) 240-Pin DDR3 SDRAM DDR3 1333 (PC3 10666)
System Memory Speed 1333 currently underclocked to 1066
System Memory Clocking 7, 7, 7, 20
Video Card Type and Speed Nvidia GeForce GTS 450 1Gig DDR5 DX11
Video Card Cooling stock
Video Card Temperature 32C idle
Power Supply Unit (PSU) Antec EarthWatts EA750 PSU
Computer Monitor Dual Dell ST2320L
Sound Card Integrated RealTek HDA
Speakers Klipsch
Headset/Microphone Altec Lansing
Hard Drive Two Seagate 500 gig SATAII's ST3500418AS ATA
Optical Drives Lite-On DVDRW x2
Keyboard and Mouse Logitech USB Optical
Modem-Router Type Arris MODEL: TM602G / Microsoft MN700
Network Adapter Realtek RTL8102E/RTL8103E Family PCI-E Fast Ethernet NIC
Printer HP InkJet 990cxi
Network Speed WD Passport 500gig USB 3.0 BackupDrive
USB Controller NEC Electronics USB 3.0 Root Hub
Gaming Console Xbox 360
Anti-virus Software Microsoft Security Essentials
Productivity Suite Office Pro Plus 2010
System Install Date 2011-01-25 21:59:23 on this drive
Computer Skill Level Certified Professional
Windows Experience Index 7.2
Favorite Game FarCry (original, 2 sucked)