These boards have proprietary software which makes them difficult to replace with anything other than original however the board can likely be repaired. I'm not questioning your repairs here but I'm curious about the voltage values of the diodes you replaced at D3 and D7? If there are no error codes then the only thing I can think is that the relays are not receiving the correct coil voltage. Unfortunately, the new relays don't have exposed coil pins like the old ones or you could measure the coil voltage from the front of the board. I'd start with tracing down the coil circuit for the high limit (left and upper relay) as they are both turned on by the same circuit. If the temp sensors are both good these two relays should turn on right after boot i.e. there should be 15VDC across their coils.
Addendum: I've heard it mentioned that the internet says to use a 9V battery to test these relays. I can't say that it doesn't work however I don't think it's the best idea because you have a 50% chance of applying power in the opposite polarity than the circuit is designed to work with. Some of the components can probably take this mis application of voltage, but I wouldn't do it to my own board.