A perplexing problem - I was away for a few days last weekend and shut down my PC before leaving, when I came back, the on-board LAN adapter on the motherboard had stopped working. I plugged in a D-Link wireless adapter and everything was fine. Figured I would run that way until I could make it to the store to get a PCI network adapter.
Picked one up tonight and did the following:
1) Shutdown the machine
2) Restarted the machine to go into the machine setup and disable the on-board network adapter - saved and exited
3) Shutdown the machine and installed the new LAN adapter
4) Restarted the machine and logged in
5) Removed the old eth0 connection
6) Started qBittorrent - runs fine
7) Started Firefox - would not load any of the default tabs

Started Thunderbird - would not connect to download mail
9) Started Virtual Box and the Windows XP VM
10) Started Chrome in the Windows XP VM - able to connect and load pages from the Internet
12) Removed the eth1 connection and made a new one
13) No change in Firefox or Thunderbird
14) Started Iron - displayed same symptoms as Firefox and Thunderbird - would not load any pages
Looked at the configuration of each of Firefox, Thunderbird and Iron but nothing seemed out of the ordinary (at least what I can see).
I did note that after making the new eth1 connection, I received the following:
"Problems occured during the network connectivity test."
"This can be caused by invalid network configuration, or problems with your modem or router"
"You might want to relaunch the configuration to verify the connection settings."
So deleted the connection and attempted to do again with all the defaults but still got the same response.
In case it helps, here is my ifconfig, lspci and lsusb output:
[me@LP ~]$ ifconfig
eth1 Link encap:Ethernet HWaddr 90:E2:BA:1B:6C:D2
inet addr:192.168.0.156 Bcast:192.168.0.255 Mask:255.255.255.0
inet6 addr: fe80::92e2:baff:fe1b:6cd2/64 Scope:Link
UP BROADCAST RUNNING PROMISC MULTICAST MTU:1500 Metric:1
RX packets:998336 errors:0 dropped:0 overruns:0 frame:0
TX packets:909999 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:1000
RX bytes:706421868 (673.6 MiB) TX bytes:320242751 (305.4 MiB)
lo Link encap:Local Loopback
inet addr:127.0.0.1 Mask:255.0.0.0
inet6 addr: ::1/128 Scope:Host
UP LOOPBACK RUNNING MTU:16436 Metric:1
RX packets:1699 errors:0 dropped:0 overruns:0 frame:0
TX packets:1699 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:0
RX bytes:234368 (228.8 KiB) TX bytes:234368 (228.8 KiB)
[me@LP ~]$ lspci
00:00.0 Host bridge: Advanced Micro Devices [AMD] nee ATI RX780/RX790 Chipset Host Bridge
00:02.0 PCI bridge: Advanced Micro Devices [AMD] nee ATI RD790 PCI to PCI bridge (external gfx0 port A)
00:11.0 SATA controller: Advanced Micro Devices [AMD] nee ATI SB7x0/SB8x0/SB9x0 SATA Controller [IDE mode]
00:12.0 USB controller: Advanced Micro Devices [AMD] nee ATI SB7x0/SB8x0/SB9x0 USB OHCI0 Controller
00:12.1 USB controller: Advanced Micro Devices [AMD] nee ATI SB7x0 USB OHCI1 Controller
00:12.2 USB controller: Advanced Micro Devices [AMD] nee ATI SB7x0/SB8x0/SB9x0 USB EHCI Controller
00:13.0 USB controller: Advanced Micro Devices [AMD] nee ATI SB7x0/SB8x0/SB9x0 USB OHCI0 Controller
00:13.1 USB controller: Advanced Micro Devices [AMD] nee ATI SB7x0 USB OHCI1 Controller
00:13.2 USB controller: Advanced Micro Devices [AMD] nee ATI SB7x0/SB8x0/SB9x0 USB EHCI Controller
00:14.0 SMBus: Advanced Micro Devices [AMD] nee ATI SBx00 SMBus Controller (rev 3a)
00:14.1 IDE interface: Advanced Micro Devices [AMD] nee ATI SB7x0/SB8x0/SB9x0 IDE Controller
00:14.2 Audio device: Advanced Micro Devices [AMD] nee ATI SBx00 Azalia (Intel HDA)
00:14.3 ISA bridge: Advanced Micro Devices [AMD] nee ATI SB7x0/SB8x0/SB9x0 LPC host controller
00:14.4 PCI bridge: Advanced Micro Devices [AMD] nee ATI SBx00 PCI to PCI Bridge
00:14.5 USB controller: Advanced Micro Devices [AMD] nee ATI SB7x0/SB8x0/SB9x0 USB OHCI2 Controller
00:18.0 Host bridge: Advanced Micro Devices [AMD] Family 10h Processor HyperTransport Configuration
00:18.1 Host bridge: Advanced Micro Devices [AMD] Family 10h Processor Address Map
00:18.2 Host bridge: Advanced Micro Devices [AMD] Family 10h Processor DRAM Controller
00:18.3 Host bridge: Advanced Micro Devices [AMD] Family 10h Processor Miscellaneous Control
00:18.4 Host bridge: Advanced Micro Devices [AMD] Family 10h Processor Link Control
01:00.0 VGA compatible controller: Advanced Micro Devices [AMD] nee ATI RV770 [Radeon HD 4850]
01:00.1 Audio device: Advanced Micro Devices [AMD] nee ATI RV770 HDMI Audio [Radeon HD 4850/4870]
02:07.0 Ethernet controller: Intel Corporation 82541PI Gigabit Ethernet Controller (rev 05)
02:0e.0 FireWire (IEEE 1394): Texas Instruments TSB43AB23 IEEE-1394a-2000 Controller (PHY/Link)
[me@LP ~]$ lsusb
Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub
Bus 002 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub
Bus 003 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
Bus 004 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
Bus 005 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
Bus 006 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
Bus 007 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
Bus 001 Device 003: ID 1058:1021 Western Digital Technologies, Inc. Elements 2TB
Bus 003 Device 002: ID 046d:c318 Logitech, Inc. Illuminated Keyboard
Bus 004 Device 002: ID 046d:c01b Logitech, Inc. MX310 Optical Mouse
Bus 006 Device 002: ID 051d:0002 American Power Conversion Uninterruptible Power Supply
Bus 006 Device 003: ID 046d:08b2 Logitech, Inc. QuickCam Pro 4000
[me@LP ~]$
Since it's three pieces of software all displaying the same symptoms, I tend to think it is something that got changed when the new adapter was installed but I don't see what it might be in the eth1 connection (if that is where the problem lies).
Any suggestions on what to try or where to look?