As in two sticks in a set, or two individual sticks?
Since it's quite improbable that after replacing MoBo with new one (was the 2nd MoBo new one?) and another set of RAM (is the 2nd RAM as a set?), you still get the same issue, where two RAMs doesn't work together but do work individually.
Oh, you have 4 RAM slot MoBo, try putting the two RAMs into 2nd channel and look if they work. E.g when at primary channel, the RAM would be in slots DIMM_A2 and DIMM_B2, put the RAM into secondary channel: DIMM_A1 and DIMM_B1.
You can also try out all configurations, albeit tedious, you might get lucky, where;
Stick small sticker to each of the RAM sticks, with DIMM1 and DIMM2 written on them, so you can distinguish which would be 1st stick and which would be 2nd stick. Then, test configurations:
DIMM 1 in 1st slot + DIMM 2 in 2nd slot - tests - yes/no for reboot loop,
DIMM 1 in 1st slot + DIMM 2 in 3rd slot - tests - yes/no for reboot loop,
DIMM 1 in 1st slot + DIMM 2 in 4th slot - tests - yes/no for reboot loop,
DIMM 1 in 2nd slot + DIMM 2 in 1st slot - tests - yes/no for reboot loop,
DIMM 1 in 2nd slot + DIMM 2 in 3rd slot - tests - yes/no for reboot loop,
DIMM 1 in 2nd slot + DIMM 2 in 4th slot - tests - yes/no for reboot loop,
DIMM 1 in 3rd slot + DIMM 2 in 1st slot - tests - yes/no for reboot loop,
DIMM 1 in 3rd slot + DIMM 2 in 2nd slot - tests - yes/no for reboot loop,
DIMM 1 in 3rd slot + DIMM 2 in 4th slot - tests - yes/no for reboot loop,
DIMM 1 in 4th slot + DIMM 2 in 1st slot - tests - yes/no for reboot loop,
DIMM 1 in 4th slot + DIMM 2 in 2nd slot - tests - yes/no for reboot loop,
DIMM 1 in 4th slot + DIMM 2 in 3rd slot - tests - yes/no for reboot loop.
This above, is the only way to test if you can run two sticks of RAM together or not.