I wouldn't worry about the voltage readings, looks like you've got you 12V, 5V and 3.3v, so power supply seems to be in order.
One thing you left out of your posting so far is your rPi, what version are you running?
When you build a HM the ATMega is blank, so your HM will do nothing. When you power your HM with a rPi connected the HM software see's the blank ATMega and flashes the HM firmware to it, THEN you have a working HM. So, you see, your problem could be your rPi is not loading the HM software for whatever reason, OR you have a HM hardware issue.
I've found the micro SD cards to be more finicky than regular SD cards. My rPi zeroW came with a microSD with raspian preloaded, WinDiskImager said it wrote the HM image successfully but the HM software didn't load. Checking the router I see the rPi grabbed an IP, but no HM web page there... head scratcher! I noticed the rPi didn't grab the standard HM IP, which sparked a thought, looks like raspian is loading? So I put the card back in my PC and sure enough the drive had the factory raspian files on it still. IDK WHY, but it did. So I wrote it again, this time took a look at the card in windows before I pulled it, saw the HM folder structure was there... NOW it works perfectly! I can't explain why it didn't work the first time, it said the write was successful....
At any rate, point being, you want to make sure your rPi is booting up the HM software before you assume its a hardware issue. The rPi will actually load the HM code and function on its own without the HM connected[, you just wont see any temperatures reported. Have you tried to connect to the HM software on the rPI? You should be able to do that if your rPi is loading the HM code properly. Or you can plug a monitor into the rPi and see what is going on directly.
EDIT: perhaps I spoke out of tern... I just removed the rPi A+ from the HM I had handy and it doesn't seem to load the HM software on it's own. I am pretty certain it DID when I tried that with my rPi B. So it might not be a sure bet that the HM software will load without the HM board connected. Activity on the wifi dongle LED's is a good indicator of life of some sort on the rPi.