Thanks for your quick response. The laptop is currently crashed, and so I'll check logs and more later. I discovered uprecords a while back, and I've had uptimes as long as 136 days. I think the current mode of uptime is around 10-20 days, but it may be longer. I do sense that it's shorter than it was before I started using uprecords, but I'm not sure, and that could be due to either hardware or a bad update.
Your idea about running W7 for a while is intriguing if a bit painful (all my stuff is on the Linux side). Still, I don't think that's what I need right now. One could view this as two problems: random freezes followed by an inability to reboot. While I don't use W7 often, I only recall one time W7 failed to boot, and it recovered nicely. Right now, I haven't been able to boot Debian since last night, although I've booted W7 multiple times. It sounds as if some state information is being written to disk on the Debian side that makes it hang up when starting ACPI (usually) or gdm3 (occasionally) or while checking the battery (occasionally).
Karl mentioned possible overheating. I let it sit overnight unplugged and tried again this morning, but it still failed. There is also no sign of overheating (fan noise, hot air, heavy-duty number crunching) when it crashes, at least as far as I can recall.
When I get a moment, I'll boot into recovery mode (that always works) and then run startx (which also works). I'll try to find any useful logfile info so I can post it here.
Oh, and Karl asked if I had any strange video drivers. My laptop has a dual Intel/ATI graphics system, but I think the ATI side and the switching isn't supported out of the box, so I've just left the standard Intel drivers in place.
IIRC, when it freezes, it's solidly dead. The screen is still as it was, but nothing has any effect: mouse, Alt-tab, attempts to get to virtual consoles. I honestly don't recall if I have blinking cursors :-%, but I certainly don't recall seeing any after a freeze.