If the system does POST without a module in that slot but not with it, that's the diagnostic - the board has a bad memory slot.  Nothing further is needed (or possible).  
Bit of backstory first. I got a free Alienware M11x R1 a not too long ago which had a dead GPU. I mean it would boot and all, but the thing would freeze and show a garbled screen the moment I tried installing GPU drivers. I tried to get that one to its max of 8GB of RAM but that didn't quite  work, though I used Corsair RAM which apparently is problematic in those. I changed its mainboard eventually with one I bought off of eBay from a Chinese seller who refuses to reply to me. It works fine for the most part. Except one RAM slot (slot 1) appears totally broke. It won't POST if a known good DIMM is installed in it. It won't POST with 2x2GB of DIMMs installed but it'll POST with one DIMM installed in slot 0. But it won't POST with the same DIMM installed in slot 1! Is there some sort of diagnostic thing I can run to make sure the slot is broken? Or is it perhaps some weird BIOS issue? It's running BIOS version A05. It doesn't have a BIOS battery.
M11x R1, broke RAM slot?