Paul: I have EXACTLY the same issues on 2 boards, but No LED lit.
I got your email, which has much more information. You're definitely not seeing exactly the same problem as the messages above, which aren't even the same as each other. I know the result is the same: a dead Teensy... but the underlying issues in these 3 messages are vastly different.
Your email has a photo with several wires soldered to the Teensy, which looks like quite a bit more than "only ever been connected to a PC".
I want to help you. I want to get this issue fully resolved. If there's any reason to believe the trouble is due to material or workmanship problems on our part (on a recently purchased board), I'm happy to send you a replacement.
But you've got to participate in finding the solution! When you simultaneously post here and send me private email, and when the two are very different, that really complicates things on my end. Saying here that you've only plugged the Teensy into a USB port, when there's clearly wires soldered in a photo in email really gives me 2 different narratives. Your email talks about soldering, which is completely different than your description here! I'm going to try to do the best I can with the conflicting info I have.....
From your email, you're getting zero volts on the PROGRAM pin and zero volts on the RESET pin, but you have proper 5V and 3.3V power. Clearly that's a very different problem than the power-related issues in message #10 above. Lots of people do lots of awesome creative stuff with Teensy, which can result in a lot of different problems. It's simply not helpful to find a forum topic with related problems and insist they're related, only because they have the same "dead" result. If anything, that's a huge distraction from figuring out what's going wrong.
From your email:
VUSB=5v
3.3v = 3.25v (Both of them)
Reset = 0.00v
Program=0.00v
Zero volts on the PROGRAM pin is almost certainly a sign the pushbutton has failed in a shorted state, or a wire or something else on the board has shorted the PROGRAM line to ground. It's also possible, but very unlikely, that the Mini54 chip could have failed somehow.
PROGRAM is supposed to have a pullup to 3.3V due to the Mini54 chip. When you press the pushbutton, it shorts PROGRAM to ground. That's what instructs the Mini54 to take control of the MK20. When it does that, it drives RESET low. Since you're also seeing RESET stuck low, my guess is the Mini54 is very likely working and doing exactly what it's supposed to do, which is keep RESET low while you continue holding the pushbutton down.
If you're willing to try troubleshooting, the thing to investigate is why PROGRAM is stuck low. My guess is something when wrong during soldering. Or maybe the pushbutton got damaged somehow (typically a physical failure in the button results in an open circuit).
You might also try connecting a fairly low value resistor, like 100 ohms, between PROGRAM and 3.3V. If there's a dead short, PROGRAM will remain at zero volts, even with 30 mA of current. If you have a voltmeter with sensitive mV scale, you might be able to see small changes in the voltage along the path the current takes, which can help suggest where the short might be.