Apple hardware diagnostics freezes at 95%

Recently my Mid-2011 iMac (default specs except 2x 4GB RAM boards were added years ago, ruing latest OS X and most recently updated days ago) has been locking up during use - a single random app would get a beach-ball - sometimes it would finally clear, and sometimes the system would lock-up hard - the dock, the hard drive icons, some finder toolbar icons, etc would vanish, the mouse wouldn't move and keyboard won't work so I have no choice but a hard reboot. iTunes would halt playback as if there was an issue accessing the disk or ram.

I booted into single-user mode, ran fsck -fy and it repaired some minor errors but the problem continued.

I booted into the apple hardware diagnostic software and at first, it was reporting 4MEM errors. The plan was to remove RAM boards one-by-one to determine which was corrupt. The test passed after I re-seated both original 2GB boards, which is odd given that they haven't moved since I bought the machine and nothing's happened that would have jolted it.

However, even though the diagnostics test passes the memory section, it freezes around 95%, the mouse becomes choppy/jumpy, and the only way to shut it down is to hard-reset.

I tried to let the machine boot normally just to see what would happen and now it auto-shuts off half-way through the boot sequence.

Is there anything else I can do to narrow down the cause? I have a time machine backup of all my files but would much rather avoid buying a whole new machine or taking it to a repair shop and wasting a several hundred.