Question: Here's the story.

There's a local sharepoint server called brksharepoint at ip address 10.2.1.40.

I had set up my computer to use google's dns because I found it to be more reliable than my local isp.

Using an app that had recently been set up I was getting 401 errors, I couldn't figure out why as I was logged into the local domain and it should have 'just worked'.

Browsing to the ip address "10.2.1.40" worked (however it prompted me for my user credentuals when I am logged into the local domain) and browsing to the computer name brksharepoint in ie 10 failed with a 404.

I then edited my hosts file to resolve to the correct ip address as I thought this was the problem - this fixed nothing.

Here's where it gets weird.

I found I could ping brksharepoint (with a wiped hosts file), and tried browsing with chrome... this worked, where ie would fail.

I then turned off google's dns and used my local gateway instead - magically this fixed everything.

What's going on here? Can I use google dns if I want to use this sharepoint server?

Thanks for any ideas - more curious than anything.

Answer: 
Can you run a local DNS server, on your router perhaps? This way you could run a lightweight client like dnsmasq to resolve local names before requesting it from Google.

What I suspect is happening is your computer tries to resolve `brksharepoint` with Google but this of course isn't a real name, so it returns an incorrect IP address (one of the standard 'name not found' webserver) or lookup failure.
You're using a public DNS server while trying to access a local address on your LAN. Set up a local DNS server that looks to 8.8.8.8 in the event it cannot resolve something. Or in your network settings, enter the local address as DNS1 and 8.8.8 as the alternate.