Tested your RAM?
This. You can't access all of your 8GB in 32-bit mode so it's likely that the faulty memory region is not accessible in 32-bit mode. Run memtest86+ for at least 1 pass.
EDIT: There's a very very small but non-zero chance that the CPU itself has a flaw in one of the address lines that isn't accessible when the CPU is not in long mode (64-bit). I still think it's more likely that the RAM is bad. Try swapping sticks out; memtest86+ doesn't expose all memory issues (just most).