KerNO is definitely compatible with Titanium HW3, but I don't know about HW4 (what I have). Could it make a difference? I don't really know what the differences in hardware versions are.

No programmatic difference between HW3 and HW4.

Would it help if I ran Ghostbuster on everything on my Titanium?

Not likely: if you used programs that don't run on the 89T, you'd get well-known and well-visible problems (no grayscale in games, major trouble with compressed programs if you're using the specific launcher or large, multi-chunk programs). than not being able to delete some FlashApps.
SuperStart cures the woes of old specific launchers for compressed programs, and usually saves space because you can just throw these specific launchers away.

1.) I seem to remember some of these things not playing nicely with one another, I don't know if I would try it. Not sure what kind of problems it could potentially cause.
2.) I'm sure it is otherwise possible, but you'd have to be messing with some low level stuff.

Erasing the certificate then deleting the OS?

That said, BrandonW wrote an utility to unbrick a calc on which that happened, though. However, I don't remember if it was 100% reliable and I think it was only for the 83+/84+

I actually just remembered the last stupid thing I did on my Titanium, and it was before all of this happened.

I was working on the token file for my project (I was working on it yesterday and that's how I remembered) and I wanted to rename it something like "8xtoks". Unfortunately, the VAR-LINK dialog doesn't let you move a file to something with a number at the front, so I decided to try using Andrew V's cmd program (a DOS-style command line interface) that allows you to do things like move or rename archived files, or delete entire folders- things that the VAR-LINK dialog doesn't let you do.

When I tried, it screwed up my calculator... I don't remember exactly what happened but it was only solved with a combination of a RAM clear and resending the OS (not sure in which order). And after that everything seemed stable, until this...

Could this be related? Or is it still more likely that I ran some incompatible assembly program a while ago too?

Deleting entire folders is possible through the VAR-Link dialog, just select the folder with F4 before deleting it

...oh. I didn't know that, thanks.

I don't know precisely what can have screwed up your calculator. There's no write protection (only a silly execution protection that complicates launching other programs), so pretty much any memory overrun in an assembly program can have immediate or delayed consequences on the system's stability.

Wait, what about the boot code? Is that protected, like it is on z80 calcs?

So, in order to make sure everything was stable again (if memory somewhere had been overwritten) what would I need to do? Do a "system hard boot"  by removing a battery and using [ON] + [)] + [-] (a key combination which I found here on UTI when I went hunting through various tech support forums)? Delete the OS before sending a new one?

I'm not sure if this would have any relation to the problem described in this thread, but I remember having some initial stability/lock-up problems with my TI-89 Titanium when I first bought it back around 2006–2007 or so, even before I even installed any of my own stuff on the calculator. Apparently, one or more of the preloaded flash apps must have been the culprit since these problems stopped as soon as I deleted most of them, and it never came back since (and I've used it regularly from that time all the way up to now).

I remember some crashes when deleting flash apps, but I think this was due to other factors which I don't remember clearly—maybe something like attempting to run TSRs without having the necessary patch installed or something.

As others said, if it doesn't act up anymore, it's probably nothing to worry about. Also, in my experience, it seems to be a good idea in general to only have loaded on the calculator what you actually plan to use (especially where things like flash apps and TSRs are concerned) to reduce the chances of weird conflicts and such problems.