BSOD! *grrr*

Well, it's either the memory or your motherboard.
Memory is cheaper than most motherboards - and is far easier to replace.

This quote seems to refer to the problem that you're experiencing (from this link: Memtest86.com - Memory Diagnostic ) Bold/Underline is mine.

Memory Testing Philosophy There are many good approaches for testing memory. However, many tests simply throw some patterns at memory without much thought or knowledge of memory architecture or how errors can best be detected. This works fine for hard memory failures but does little to find intermittent errors. BIOS based memory tests are useless for finding intermittent memory errors.
Memory chips consist of a large array of tightly packed memory cells, one for each bit of data. The vast majority of the intermittent failures are a result of interaction between these memory cells. Often writing a memory cell can cause one of the adjacent cells to be written with the same data. An effective memory test attempts to test for this condition. Therefore, an ideal strategy for testing memory would be the following:

1. write a cell with a zero
2. write all of the adjacent cells with a one, one or more times
3. check that the first cell still has a zero

It should be obvious that this strategy requires an exact knowledge of how the memory cells are laid out on the chip. In addition there is a never ending number of possible chip layouts for different chip types and manufacturers making this strategy impractical. However, there are testing algorithms that can approximate this ideal.

Sounds to me that the chips are letting information "bleed" over into adjacent chips - and the soft reset doesn't flush this out (while the hard reset does).

My guess is that it's the memory modules themselves - but that will have to be determined by trying other memory chips. Your money - your call. Good luck!