For all I know, it was a miracle, brought about by the power of internet community. I could barely sleep last night, and at 6 AM I popped out of bed to check and see if anyone had sent suggestions. And you had! I took krasota‘s suggestion and hooked up an external monitor and powered the laptop on. Well, somehow I not only got a display on the external monitor but also a display on the laptop screen. It appears to have healed itself overnight!
Of course, I quickly backed up everything I’d been lazy about backing up recently just in case it was all a fluke, but everything still appears to be working normally.
And now that I’ve gone through the trouble of disconnecting the monitor from my Dell desktop, I have a second monitor to use with my laptop when I’m at my desk (until I need to use my Dell for something, which is increasingly rare anymore). Bonus!
Thanks to everyone who commented with suggestions and sympathy. Your support healed my laptop!