This tends to indicate that your environment requires a proxy server to reach the internet and your organization blocks DNS resolution for Intranet sites.
Typically, this isn't a problem because Fiddler is defaulted to chain to the upstream proxy gateway it finds in IE's proxy settings when it starts up, which means that if Internet sites work before Fiddler starts, they'll work after it starts because Fiddler will use the same proxy.
The one exception to this is if your IE settings point to a proxy configuration script using a file:// URL. Fiddler (and WinHTTP-based applications) doesn't support PAC files that use that protocol for retrieval.
When Fiddler isn't running, what do you see inside IE's Tools > Internet Options > Connections > LAN Settings?
What do you see in Fiddler's Log tab after starting it?