I assume you’ve tried basic elimination, by testing with different parts & peripherals removed?
It’s a hassle of course, especially after you’ve already settled in to using the system, not to mention how tedious it is to run memtest for days on end just to achieve sufficient confidence that you’ve proved a negative.
I’m not as hardcore about this as Jeff Atwood, but I’ve learned not to discount anything as potentially being the cause or at least a trigger for all kinds of issues. Besides obvious things like RAM modules, OTOH I’ve had at least one internal memory card reader, one USB bluetooth dongle and one (SATA) SSD turn out to be the troublemaker; usually something much easier to replace than motherboard+almost everything. (And unfortunately it’s usually been easier to just replace or just get rid of the triggering component rather than hope for a software fix, even if the issue ultimately was with software.)
The cold lockups or the case being touch-sensitive don’t sound like one of those easily solvable ones, but since there’s a plethora of symptoms, perhaps some still might be, and are just hard to see from the mix.