There is a lot of paperwork along side it. Does it give error codes to help localize the fault?
I have what we call a hydronic heating system. It uses hot water to heat the house and the domestic hot water is produced by a heat exchanger with the heating water. There's a boiler, 2 pumps, lots of water pipes. I use propane for the power. Originally there was both an indoor wood burner and outside wood burner that added 2 more pumps. In other words, aside from my heat source, it might be similar to your system.
My control panel went bad about a week after I bought the place in 2010. It was cycling on off and no heat. Similarly, it was obsolete, but a new panel was only $200, it was freezing outside, so I got it. Later, I took apart the old control panel It was less complicated than yours (house was built in 1993, but similar. The solid state stuff rarely fails. The problem was the small "logic" relays -- about half the number of orange things on your board.
Sorry for the long lead in to my suggestions:
1) Those relays look like standard footprint control voltage level relays. Identical brands may not be available, but there are inexpensive substitutes.
2) If you cannot localize the fault to a single circuit/couple of relays, buy a bunch. Otherwise, buy what you need to replace them and replace suspect relays in that motor circuit.
3) The motor may be fine, but there is probably a boiler fan and other things that need servicing. My boiler fan gets oiled once a year. A replacement is about $100.
4) Check that the pumps are working.
5) My system had a bypass valve between boiler input and output. Its purpose was to give a quick temperature rise in the boiler and reduce water condensation in the flue. At 30 years, it stuck open. I got rapid cycling, an overheat situation, and the house temperature rise was limited to only about 10° above outside ambient. I removed the valve and added a drain to the flue. It has a water trap to prevent gases from entering the house.
If your system is like my system, I would look at #5 first, then #1. Solid state devices rarely fail. Mechanical (e.g., blowers, relays, and valves) are the most likely failure points.