As you have had the machine booted up into Safe Mode with Networking then that would have eliminated your antivirus or a possible infection as the problem, providing an infection hasn't disabled any services.
I wonder if it's just Ultimate that has an icon for the Ethernet as Home Premium doesn't.
Even though the other machines have no problem connecting, a power cycle of the modem and/or router can resolve a problem for a machine that will not connect.
To perform a power cycle, switch off the modem (if applicable) and router as well as any computers then disconnect all cables to the modem and/or router for a couple of mins.
Reconnect the cables, switch just the modem on if applicable and wait for all of its lights to come on and then do the same for the router.
Switch just the affected machine on to see if there's a connection.
If it's still a no go then do the following steps and let us know if any or none resolve.
Even though you have run Windows Repair, open a command prompt as an admin by going Start - type cmd - right click on cmd and select Run as administrator - accept the UAC then enter these commands -
netsh winsock reset catalog
netsh int ip reset resetlog.txt
ipconfig /release
ipconfig /flushdns
ipconfig /renew
ipconfig /registerdns
shutdown /r /t 00
and then see if you can connect after the reboot.
Go Start - type devmgmt.msc and press enter then in Device Manager click on View/Show hidden devices and look for any yellow alerts, red crosses or black downward pointing arrows.
If they are okay then go Start - type services.msc and press enter then check that the following services are showing as Started and Automatic or Manual -
COM+ Event System
Computer Browser
DHCP Client
DNS Client
Network Connections
Network Location Awareness
Remote Procedure Call (RPC)
Server
TCP/IP Netbios helper
Wired Autoconfig is set to manual.
WLAN AutoConfig
Workstation
If a service is not running, click on it to highlight then click on Start (top left).
If it fails to start then right click on the service to open its Properties and check the Dependencies and that each of them are running.
Any Dependencies that aren't listed in services can be found in Device Manager/View/Show hidden devices/Non-Plug and Play Drivers but if any in there are problematic, you would have seen a yellow alert next to Non-Plug and Play Drivers.
If everything still checks out then go Start - type eventvwr and press enter.
When Event Viewer has read the data you will be presented with Critical, Error and Warning etc.
Click on the name Error then on View All Instances of This Event in the lower right pane and look for any DHCP, network adapter or network service errors.
