C023 is responsible for smoothing the half wave rectified DC from D012. If it's bad, there will be lots of ripple on that supply which feeds the power relay, and standby 5v and 12v supplies. The added load of the power relay may be enough to pull down this supply down too low to work. I wouldn't waste any more time looking for other problems until you have a known good cap in there. If you're ordering parts, I would get C025 and C026 too since they're also working 24/7 and could be contributing to the problem.