network

Clarifications

and see if your network is showing whether its lan access or lan and internet access.

If its showing lan and internet you should be able to connect.

Also, is your firewall set to block all?
Do you have any second party firewalls installed?

Have you scanned for virus/trojan? Is the network light blinking a lot when you try to connect and fail?

Can you ping an ip address?
ping 74.14.207.99 (this is google fyi)

Here is a link to a site to fix winsock errors, but since it works in safe mode, I very much doubt it will help.
http://www.mydigitallife.info/2007/06/18/repair-and-reset-windows-vista-tcpip-winsock-catalog-corruption/

One last note: you may want to edit this post and remove your hotmail address unless you reallllly like spam.

TCP/IP stack Winsock settings in Windows Vista may get corrupted, causing errors and problems with Internet connectivity. Corrupt Winsock or Windows sockets configuration can be due to a lot of reasons such as installation of a networking software, or due to virus, trojan or malware infection, or sometime even due to disinfection of spyware by security software.

When Winsock corrupts, the networking errors that you may face include unable to surf the Internet with ?Page cannot be displayed? error message in Internet Explorer or AOL even though the DSL/ADSL/cable Internet connection is connected. Sometimes, Windows Firewall/Internet Connection Sharing (ICS) service is terminated as well.
To repair and reset the Windows Vista
1.Click on Start button.
2.Type Cmd in the Start Search text box.
3.Press Ctrl-Shift-Enter keyboard shortcut to run Command Prompt as Administrator. Allow elevation request.
4.Type netsh winsock reset in the Command Prompt shell, and then press the Enter key.
5.Restart the computer.
What netsh winsock reset command does are it resets Winsock Catalog to a clean state or default configuration. It removes all Winsock LSP (Layered Service Providers) previously installed, including the potential malfunctioned LSP that causes loss of network packets transmission failure. So all previously-installed LSPs must be reinstalled. This command does not affect Winsock Name Space Provider entries.
Note: To check which LSPs installed on your Vista system, use netsh winsock show catalog command.
It?s also possible to reset TCP/IP Internet Protocol stack.

Please post back if you have any more problems or questions.

but safe mode with networking yes. Most people do not use this option a lot, since safe mode is usually used to test for bad drivers, malware, etc.

1) Try to install the latest driver for your network card. Using a web browser in safe mode is annoying, but it works enough to get drivers downloaded.
2)Look for an updated chip set driver for your motherboard.

[option][edit] these are XP instructions, but should work in vista.
Since the computer allows web access in safe mode, while the computer is in safe mode, right click on My Computer and choose "Manage." On the left hand side of Computer Management, select Device Manager, and on the right hand side expand the Network Adapters. what card do you see listed?
now, boot into normal mode and do all this again. Any big yellow ! on any entries?

[edit2]
winsock error 10013 is a permission error. On a whim, disable UAC and then try to access the internet.
http://www.petri.co.il/disable_uac_in_windows_vista.htm
how to disable UAC.

Also I assume you are using IE to browse, does Firefox work different? And you have done a full AV check?

Winsock error info:

WSAEACCES (10013) Permission denied.

An attempt was made to access a socket in a way forbidden by its access permissions. An example is using a broadcast address for sendto() without broadcast permission being set using setsockopt(SO_BROADCAST).

http://www.dataenter.co.at/common/winsockerror.htm