Have you tried adding the site to your "Trusted sites"?
Do you use any proxy server?
May be your user profile is been corrupted on that computer.
You can try this to see if it helps. Go to your Network Connections area in Control Panel. Right click your LAN>properties>Internet Protocol TCP/IP>Advanced Tab. Make sure their are no DNS Suffixes applied. Or you can compare the settings with the good working computer/account to the one not working and see if the settings differ.
other stuff to try: open cmd prompt> IPconfig /flushdns.
• Check, or double check, if the loopback check is disabled
• Check if you can log in from your client pc instead of logging in from the server
• Disable "enhanced security" of the IE on the server (for test purposes only) and try it again
• Add SharePoint site to the intranet zone in IE
• Log in with "the other user" and check the permissions of your account (like it is done here: http://teamcollab.wordpress.com/2010/01/25/checking-permissions-in-sharepoint-2010/)