It had been sitting for maybe a month with no power and a bad clock battery. I opened it up to swap the battery, which works fine; it remembers the date and time no problem now.
Since I had it running, I figured I'd play a bit of Bust-A-Move 4, so I popped it in and tried to boot it. The console recognizes the disc, shows the Sega licensing screen (and the correct version with the Windows CD logo), but, right when it's supposed to start the game, it loads the main Dreamcast menu. No matter how many times I launch the game, or cycle the disc lid, or cycle power, it keeps doing this.
I gently cleaned the lens with a cotton swap soaked in alcohol, reseated the PSU, and reseated the GD-ROM; I even checked the game disc for disc rot, and it looks pristine.
What it will do, however, is load 240p Test Suite from an old CD-R. Sadly, I don't have another US game disc to test with, but I can track down a boot disc to try one of my Japanese games.
So what can I do? Is it as simple a fix as cleaning or greasing something? Do I need to get a replacement GD-ROM assembly? Where would I even get one now? They don't seem to be as available as PlayStation CD assemblies (nothing on Amazon, eBay), and GDEmus (as much as I'd like one) are expensive and not readily available.