Alright, so, about a week ago, I got a Nest thermostat and installed it
with the 4 wire setup we have. It worked just great for 3-4 days.
Everything was wonderful and I loved the new thermostat. I decided to
get on the internet and read that the Nest works best with a common
wire. So, I noticed we had an extra wire (blue) behind the thermostat
that wasnt used. I installed it, but nothing happened because the wire
wasn't attached at the furnace.

Here's where the trouble begins. I installed the blue wire, but forgot
to put the door on, which activates a switch, so the system never came
on. Of course, I totally forgot about this, so I thought I messed
everything up. So, I put the wires back the way they were, closed the
door, and the system worked, but with a hitch.

The problem: now when the thermostat calls for heat, the burners will
turn on, then after a minute or so, turn off, then the blower will stay
on for a couple more minutes and then everything will shut off. However,
it doesn't always do it, and seems to do it more when I call for higher
heat. The nest will briefly flash a yellow/orange light, then the
voltage and amperage will go down almost to 0. Almost like a switch has
been flipped.

I called Nest, they walked me through a bunch of troubleshooting steps,
determined it was a faulty base, so I replaced that, and it still
did it. One note: during troubleshooting, they had me reverse the white
and yellow wires and that made the system work fine, but gave me no
control over the heat (basically reverse the heat and cool wires, so
kept the heat on).

They told me I had to install a common wire since it sounds like a power sharing issue. Turns out, that extra wire was the common wire and I had it right when i forgot to close the door. Installed that wire, which went great, but the problem still
happens! I called an HVAC friend, and he told me to open the door, hold
the switch manually, and see if that works. That time the system turned
on and stayed on perfectly fine. He said it sounds like there is
something that's restricting air flow and a limiter switch is engaging
to prevent overheating (thats why the burners turn off and the blower
stays on a little while after--to further cool the system). He told me
to make sure all the vents are unblocked and that there are no filters
in. I did that, it still happens. I cant be sure, but it seems like it helped a bit.

Anyway, what the hell could possibly have happened? What did I do? It's
not an emergency since the house eventually gets to the temp I set it
at, but I'd like to figure this out. To recap, the problem seems to
happen more often when the heat is set higher (69-70). According to the
Nest, voltage and amperage suddenly go almost to 0. The problem seems to
be alleviated when the door is open and I hold the switch manually. The
system works fine when the heating and cooling wires are reversed,
though this gives me no control over the heat (Nest troubleshooting
step).

Thanks a lot for taking the time to read this! :)