This might look like an easy one "get yourself different memory chips", but I'm not convinced:
I set up 12.04 64bit on a new board with 8 GB of memory plugged in. I can see all 8 GB in the BIOS (it says: 4 x 2GB plugged in), even though the self memory tests (run before I enter the BIOS) shows only 3820 MB.
If I launch Ubuntu, system info also displays 3820MB, but if I run the memory test (-> System Testing), it fails with
Meminfo total: 3533740 kB DMI total: 8192000 kB Accuracy: 43.00 Memory totals not close enough
Ooops, there are my 8GB !?
So, I'm desperately looking for any leads from here....
ps: double checked that I installed the 64bit version...
I can't comment due to being new so I'm leaving this here.
If the POST (power on self-test) is showing 4 GB, that's a hardware or firmware issue. Have you double checked the modules are correctly seated? I don't know how to get Ubuntu to pick up the memory - but if it were my system I would be looking at the hardware.