Macbook Pro (2010, OSX Sierra) has started prompting me to enter password for DHCP again and again and again
You've got a trojan! 
Look at the Directory ~/Library/VideoFrameworks
The Trojan collected your keychain and browser-data there.

The program itself resides in ~/Library/RenderFiles

You can stop it with
launchctl stop fr.handbrake.activity_agent

Did you install handbrake as well or just makemkv?

I would recommend to make a clean install of osx or install your time-machine backup from before the installation of the program.

Update: I cannot comment here, so I try to edit my answer with additional information:

The trojan collects at least the following data:


Keychain files (saved passwords in OSX)
Personal data from every browser on your system including saved passwords
Screenshots


So you really should check which passwords you saved in the keychain and the browser and change them immediately on another computer. You can find the data that it collected in the directory described above in several zip-files.

Do you remember where you downloaded handbrake? Did you use the update function?