Lennox G23Q3/4-100-2 And Ecobee4
It has hard to see that mess of wires. I believe what they did was wire nut the C to the wire that goes out to the outdoor unit contractor. That works fine as long as the blue wire is hooked to Y on the thermostat. The blue was your Y wire for cooling. But then what do you use for common?You are going to need 5 wires from your thermostat to your furnace. Just hook up R to R, W to W etc.  then on the C and Y terminals at the furnace you will attach the red and white wires coming from the compressor so you will have 2 wires on each of those terminals.