Actually i NEVER had this problem until i updated my video card. Currently running a 6600gt.
I'm also running the high-res patch, but other than that, my specs are comparable to yours.
I shall do a series of my own tests, but i've found that alt tabbing while in battle wont make the battle crash, and subsiquetnly, the next battle wont crash, either.
I think staying on the world map or in the field for several minutes aleviates any stress ff7 is reeling from, and so the crash doesn't happen, but i have to double-check this.
As for the "takes a screenshot" thing, i assume that is correct, as that's what it has to do to swirl Cloud's face after the FMV where he's flying down towards Sephiroth.
I shall edit this post when my computer isn't busy doing anti-virus scans =P
[edit 1] it MAY be service pack 2, also: I don't think i had that before, either. I'm gonna see if i can get my hands on a non sp-2 version of pro and install that (I gotta reinstall my OS soon anyway, my compys been acting farked up)
[edit 2] Okay, ti happens on both the world map, AND in the field; however, something interesting happened in the field. I alt tabed out, and right after i alt tabed in, i went into a battle no problem. So i alt tabed out after, and then, next battle, BAM, it crashed to the desktop.
I had assumed it was the high res patch. hm.
I have access to a few other video cards, and i'll try those out, as well. I'm still thinking it's a high-end video issue. See, i have a whole WEBSITE designed around making screenies of ff7, and i can state with 100% accuracy that this never happend with my voodoo (though i had 95 at the time...), and only occured less than 0.5% of the time under my mx 400.
I have the next 2 days free, so i'll be able to test lots of stuff on my own end for ya =) I'd love for this to get fixed, because it's been annoying the piss out of me.