If we read your manual correctly it states to install the PEK.
https://www.ecobee.com/wp-content/uploads/2013/12/ecobee3_InstallationGuide.pdf
You can also look here:
https://www.stevejenkins.com/blog/2014/09/how-to-install-an-ecobee3-smart-thermostat/
And a guide to the wire color codes is found here:
Why are the white and orange wires both connected to my thermostat's W terminal?
That said if you are looking to get around the PEK - of course I can understand that you see 'No Control Board' or Terminal Connections but simply a bunch of things wire nutted together, that maybe this is why you skipped that item.
In order to do this - you need 24VAC for that common wire and it should follow the color code for the common wire [BLACK] at least black tape both ends of your blue wire if you can't pull a black wire.. (as this tells people what circuit in the HVAC it is supposed to be) , of course that is only if you are interested in doing it right.
In Picture number 2 You have a Green , White, Red and Black wire coming down from top left. Now since there is not a real drawing of what is where and how it is hooked up and your pictures are a bit difficult to trace the wires ..
I am guessing that the Black wire is the 24VAC common that you will need to connect to - it appears to be wire nutted in the back to a brown or purple wire - I am guessing that goes to the condenser unit. First check it for voltage with a volt meter on AC setting and measure between that wire and the frame screws of the unit. Do not hold the meter by the metal leads - hold the plastic of the leads and measure - do not touch any metal with your hands! You can get electrocuted or shocked.
After measuring and making sure it is 24 Volts AC - you can hookup your blue wire as long as you taped a black band around the end with black tape - to identify it as really being a black wire. Now you have the proper voltage and wire.
EXCEPT you already hooked up stuff previously and let the smoke out of something, so depending on how much smoke was let out.. your unit should be able to run.
All of this said : Your system should work if you did not burn up anything previously.
Yes, you are right on track here
Simply connecting the light blue wire to the C terminal on your furnace control board (with the furnace turned off at the service switch or breaker, of course) will get you a C wire for your new thermostat. You are also correct that the cable with the yellow and dark blue wires connected in it goes off to your air conditioner (outdoor unit); it is what carries the signal to the air conditioner that calls for it to run the compressor.
Best Answer
The Beckett GeniSys™ Advanced Burner Control is used to control the operation of the furnace, and does not appear to supply an external
C
terminal. However, you may be able to power the Ecobee using an additional 24Vac transformer.If you have an A/C system that the Ecobee is controlling, you can power the Ecobee using the transformer in the A/C system. Just connect the
R
wire from the A/C toRc
, and run aC
wire from the A/C to theC
terminal on the Ecobee.If you're not controlling an A/C system, you'll have to use an external transformer (or if there's one in the furnace). If there's a transformer in the furnace (in the control box with the
CYGR
terminals), then you should be able to use that (assuming it's connected to power on the primary side). Simply run a (new or additional) thermostat cable from the furnace up to the thermostat. Then wire it as follows:R
andRc
on the Ecobee.R
terminal on the control box in the furnace, to theRc
terminal on the Ecobee.C
terminal on the control box in the furnace, to theC
terminal on the Ecobee.Assuming the transformer in the furnace is powered, that should get you up and running.