Random shutdowns, Macbook Pro Early 2008
Negative shutdown codes are hardware related.  If Apple Hardware Test is telling you that there was an issue with memory, you can be quite certain that the test is accurate.

Re-seating the RAM is not a sufficient test.  You need to remove the memory modules and test each one independently in each of the slots.  If you have two modules and two slots, you will perform four tests in total.  Make a note of what fails where.

What you are testing for is either a bad memory slot or a bad module.  If your memory slot is bad, you'll need to replace the logic board.  If the memory is bad, you will need to get a new module.

How will you know?

If all memory fails in one slot and not another, it's that slot.  If one module fails in both slots, it's that memory module.