I'd add to your list the following
Wireshark - to understand your network along with individual boxes on it.
The entire Sysinternals suite. It's a Swiss army knife of tools and utilities that help you analyze boxes to solve problems.
And finally, as a dev, I love the humble tracert. When tech support calls me for one of my apps, that it has trouble connecting to a database, I have them run a quick tracert. It always solves the problem, misconfigured dns settings on the client.
