keyboard not responding

The keyboard is technically a USB device on an internal bus with some other hardware (on 2018+ models it's on a T2 bus with just about everything onboard; for 2016 I don't know how much of the hardware is run through the T1).

However, I'm fairly certain that the keyboard and trackpad appear as a single USB device, so if the backlight and keys aren't working but the trackpad is, it seems extremely likely it's a hardware problem in the top case with the circuitry that connects the keyboard. That said, your experience with having it kick in for a bit when you plugged in an external is rather odd. Things you could try if you haven't already:

1. Unplug absolutely everything from the computer and boot into Recovery Mode and see if they keyboard works there. This will rule out a software problem. If it does work in Recovery mode, something is wonky with your MacOS install.
2. Unplug absolutely everything from the computer and reset the SMC and see if that makes any difference. (I believe on your Mac you shut down then press and hold left-control, left-option, left-shift, and the power button for 10 seconds.) Power it on without anything attached (to rule out some other device causing problems) and see if that helps. If they keyboard won't respond even to do the SMC reset, that's a bad sign.
3. If you can get it to reset the SMC but it doesn't help, it's a long shot but try resetting PRAM as well, again with nothing plugged in.

If none of the above help, I have to think that it's just a run-of-the-mill hardware failure and it working briefly when you plugged in an external was some kind of freak coincidence.

First: When you say you did them with an external keyboard without success, do you mean that the internal keyboard still didn't work when booted into Recovery Mode, and that the keyboard still doesn't work after 2 and 3, or that you couldn't get it to reset PRAM or boot into Recovery Mode? (I don't think you CAN reset the SMC with an external keyboard.)

I'd be in the same mental place as you as far as thinking it's a software problem, but here's the thing:

If the keyboard doesn't work when booted into Recovery Mode, it's not "just" a software problem. That's a completely independent OS from the one you normally use, and has fixed and very limited software. So if the keyboard doesn't work there, it can't be a software problem unless whatever it is will affect every MacOS install on that computer (in which case it's at best a hardware issue prompting a software problem).

You could also try this to confirm: Unplug everything, select "Restart" from the Apple menu with the trackpad, and hold down the Option key. You should get an boot disk select screen. If you don't get this and it boots normally, again, it can't just be a software problem, because that process happens before the OS has even started loading. If they keyboard isn't recognized at that stage, there's something wrong with it.

Yet another thing you could try: Hold down the hardware power button for about 10 seconds. The Mac should hard-power-off without any warning. As above, this is a firmware-level operation and doesn't involve OS-level software, so if it doesn't work then the power button isn't responding to button pushes at all.

One thing I didn't ask is how you're connecting the external keyboard--USB with a USB-C to USB-A adapter, or something else?

Two other things I didn't suggest before:

One, have you tried running Apple Diagnostics? It requires holding down the D key on reboot, and I'm not actually sure whether this can be initiated with an external keyboard if the internal keyboard won't do it, but you can try and it might tell you something if the T1 diagnostics fail or something.

Two, go to About This Mac from the Apple menu, then click System Report... in the window that appears. Go to USB and see what all is in the device tree at the top, and if there's anything unexpected or off-looking in the same tree as the trackpad+keyboard in the detailed list (unknown or missing device or something).

Just to note, it's hypothetically possible, if the keyboard is under the T1 bus, that there's something going awry with the security chip or at the USB controller level that isn't hardware in the sense that it's a broken wire and could change with MacOS or BridgeOS version or something, but isn't really software in the sense that you can just reinstall something to fix it. Resetting the SMC is about the only step you have available to resolve an issue like this, but if they keyboard is unresponsive so you can't, resetting it won't be easy.

I was able to reach recovery mode, but only by using the external keyboard. The internal keyboard remained non-fucntional in recovery mode.

As weird as this seems given the sequence of events you described, this essentially confirms it's at best a firmware issue, and more likely a hardware issue. You were booted into a completely separate OS, so anything software-level would not have followed you to recovery mode.

I went through the steps(holding down the suggested keys on startup) to reset PRAM and SMC. Nothing seemed to happen differnt from a normal start up.

This is no surprise, as the keyboard is unresponsive. I was guessing that those key commands might not work from an external keyboard.

I wasnt able to get to the boot select screen, i imagine because the internal 'option' key was not responding.

As you say, yes, the keyboard is dead even at the firmware level, so this didn't work.

"Yet another thing you could try: Hold down the hardware power button for about 10 seconds. The Mac should hard-power-off without any warning. As above, this is a firmware-level operation and doesn't involve OS-level software, so if it doesn't work then the power button isn't responding to button pushes at all."

This works. THe power button works fine. It seems to be the only key that works.

Interesting, but I wouldn't take this as diagnostic, since I don't know how the power button is wired. It's entirely possible it is independent in some way of the rest of the keyboard. (If this is a Touch Bar Mac it's not at all surprising, since it's definitely an independent device.)

I ran [Diagnostics] a few days ago with the external keybord connected and found no issues.

"Two, go to About This Mac from the Apple menu, then click System Report... in the window that appears. Go to USB and see what all is in the device tree at the top, and if there's anything unexpected or off-looking in the same tree as the trackpad+keyboard in the detailed list (unknown or missing device or something). "

Nothing unusual.

Was worth a shot, but not surprising, and doesn't tell us much.

At this point, I just don't see how it's not a hardware problem. It's obviously intermittent, so maybe whatever had it working for a while was coincidence, or maybe it somehow did something with the USB bus that kicked it in, then the OS install did something that triggered the issue again.

There is only one thing left that I can think of other than having someone replace the top case, but if you're not very comfortable inside an Apple laptop you're more likely to break something new than fix anything, and it's a long-shot:

If you open up the computer (iFixIt.com has great tutorials if you want to see just what you're in for; it isn't simple), disconnect, and reconnect the battery, this would (I think) be a brute-force way of resetting the SMC without a functioning keyboard, and hypothetically could change something. Even if it did it's probably temporary, though.

You'd be much better off just getting it professionally repaired.