We are getting to the point where component level troubleshooting may be necessary.
There has to be a DPDT relay in the K2 socket. All of the DC power for the system goes through K2. I know that you substituted a 120 VAC coil unit which will not activate because the motherboard is set up for a 24 VDC relay coil, so the system is running on the battery charger. It should still function as long as there are not many cards plugged in and no other loads on the panel. The battery charger can supply only a limited amount of current. It has to be that way because it is designed to charge sealed batteries. Those can only take so much charging current.
I am going to back up and verify some things on my end. I will get back to you as soon as I can. This weekend is busy for me. I am an officer in the local MTB club and will be putting our display tent up at the 12-hour race on Saturday. So it may be Sunday or Monday before I can get back on this.
One thing about relay substitutions. Putting an AC coil relay in place of a DC coil relay can cause circuit failures. The typical AC relay has a much lower coil resistance than a DC relay. In an AC circuit the inductance of the coil determines its impedance and the amount of current it draws. In a DC relay coil the wire itself develops the resistance and determines how much current it will draw.
The relay that goes in this board has a coil resistance of around 650 ohms. An AC coil relay can have a DC resistance of 100 ohms or less. That causes it to draw much more current from the circuit that controls the relay. In the 2001-8023 there is one little transistor that controls the relay (Q1 on the motherboard). It could easily be overloaded by an incorrect relay. In equipment I have repaired over the years I have seen these little transistors just vaporize leaving only the 3 wires attached to the board. That does make troubleshooting easy though.