Sorry to open this thread up again. I have a very similar issue that may be closely related. My Mac Mini 2011 with Intel i7 and 6630m randomly reboots during startup and normal use. Sometimes I can run Blender on it heavily before it fails, but it always does after some amount of time. I have replaced the PSU as well as the HD cable along with putting an Intel SSD inside. I hear some people talking about cold solder joints on some chip, is that the Intel BD82HM65 Platform Controller Hub? If I were to pursue the logic board repair would this be the first thing to try? Thanks in advance for everyone's willingness to help!
Restart the computer and hold CONTROL + COMMAND + P + R to do a PRAM reset. The screen will go dark then come alive again. Otherwise you can buy an inexpensive MacBook Air keyboard on Amazon or Ebay.
If anything that sounds like a properly functioning solenoid. I made you a schematic: Maybe there is a blockage in the steam wand; the steam getting released after the function is shut off sounds like it is getting blocked on delivery to the cup. Its pretty common for there to be milk dried in the steam arm if it's not purged after steaming. Hope this helps, Timothy