I forgot to ask if you could also run the command
route print and post the output of that as well.
Looking at the ipconfig /all of the good computer, it looks as if that has had connectivity problems as well, as Windows creates a MS ISATAP adapter whenever it has problems getting an Internet connection - which is why there are quite a few duplicated ISATAP adapters.
At your leisure on the good machine, go Device Manager/View/Show hidden devices/Network adapters then right click on all but the original ISATAP and select Uninstall.
There won't be much point in doing that on the affected computer yet, but I noticed there weren't as many duplicated ISATAP adapters on that one as there were on the good one - which could either mean that Windows was able to connect or that function was no longer working ??
Were you able to run the ESET and/or the .NET Framework Repair Tools and have you contacted your ISP yet to see if you are still broadcasting Citadel.
As a DHCP IP address has been assigned to the Network adapters and that you can't still connect in Safe Mode with Networking, would suggest a firewall and the only firewall still active in that mode is Windows Firewall.
Depending upon the results of ESET, .NET and your ISP, you may be able to play around with the firewall settings, but I'll leave Shane to advise on those.
http://www.howtogeek.com/112564/how-to-create-advanced-firewall-rules-in-the-windows-firewall/Probably best to create a restore point first should Shane wish to eliminate the firewall as the cause.
I don't think at this point it is worth assigning a static IP address, but MAC Filtering in the router for the affected computer could be something worth looking at where you add its MAC address to the filter, which is sometimes a requirement for Internet connectivity but being able to ping Google throws a lot of diagnostics out of the window.
This program has had some success if none of the above have restored connectivity - thing is, it doesn't tell you what it has fixed when it has and we would still be in the dark
http://www.majorgeeks.com/files/details/complete_internet_repair.html