In this case it seems to be limitation issue, checking all the components you mention I noticed that the Intel® Desktop Board DP43BF that you have comes integrated with the Intel® P43 Express Chipset (Intel® 82P43 Graphics and Memory Controller Hub) ARK | Intel® P43 Express Chipset (Intel® 82P43 Graphics and Memory Controller Hub) that only supports DDR3 800/1066 and DDR2 667/800. This chipset as you tested can run memory modules at 1333MHz but whenever you add 3 or more memory modules it stops working.
If you planning to buy more memory sticks take into consideration that the chipset supports DDR3 800/1066 or DDR2 667/800, so what you can do is to buy 4 memory modules according to what the chipset supports or to stay with the 2 memory modules of 1333MHz.
Thanks for the reply.
Sorry for not mentioning this previously but I also tried running the new modules (CMX2GX3M1A1333C9) without the other ones, didn't work.
So I'm wondering what else could play into account here that these don't work (assuming they aren't broken) ?
If you just inserted the two new DIMMs into the two available sockets, you may have a mismatch that will not work. Try putting the original two DIMMs in the connectors for one channel and the two new DIMMs in the connectors for the other channel.
Hope this helps!
Thanks, but I've tried every possible combination (also without the old DIMM's as stated above), didn't work.