Installed NTA on a brand new Server 2012 r2 box, but the service won't start.

The pop-up is masking the text of the configuration window. Does it say the network path is not accessible to NTA, and hence it cannot backup? Have you tried specifying a local folder for backup as well?

Yes, perhaps the little yellow exclamation means "you can't do that" more than "caution." I had missed the bit of documentation that says,

• Make sure you save your flow data on a dedicated disk.

Ooop, time to rebuild the server so I can put the flow storage database on a separate disk.

NTA wasn't able to see a .dll so it was failing. Fix was uninstall / reinstall NTA.

Hold on... The little exclamation mark indeed means ''caution, or not recommended". The problem might be in your backup folder, I see that you are trying to backup on network location. This is OK to do so, but make sure the shared network location is in same windows domain (perhaps other sharing options may influence it as well).