Ok, so that's not normal, but lets try something else.
Was this system running with a DIFFERENT pair of sticks, installed in the correct slots, before you got these sticks, or is this the first attempt to get this system running?
Does the system POST when you install only ONE stick in the A2 slot, which is the slot closest to the edge of the motherboard? If yes, then try the other stick there as well. If both sticks allow the system to POST try them both individually in the B2 slot. If it works with only one stick installed, regardless of which stick it is, in that slot too, then try both sticks in the A1 and B1 slots at the same time.
This could be an issue of a CPU cooler that is too tight, or is too tight on one side or in one corner, unevenly, which can cock the CPU in the socket and cause it to either short a pin or break contact with a pin, and that's enough to cause trouble with the memory slots. I've seen this MANY times. Are you running the stock cooler or an aftermarket cooler?
The fact that it will run with memory in the B1 and B2 slots doesn't change the fact that the cooler could be an issue with dual channel operation and sticks in the same channel DIMM slots, so I'd look at that.
You could also have bent pins on the motherboard socket. If this is the first time this system has been put together and is the initial attempt to get it running, I'd take it back apart and check very closely for that.