I did get it going again, but it's not entirely good news, arimanius. I'm now convinced my problems are at least partly resulting from bad hardware, and I'll have to exchange my unit.

I finally removed and reinserted the battery enough times that my 770 started holding on long enough for the Linux flasher to get started. It flashed Nokia_770_SE2005_3_2005_51-13.bin smoothly and rebooted. Then it showed the "NOKIA" splash screen at middle brightness for about 4s, went to full brightness for 1s and cut-off, darn it! After 5-6 more cycles of flashing and cutting off the same way, a miracle happened and it booted. Once up, it survived all the normal sleep-wake and switch off-power on transitions without problem. However, starting the "Date and time" or "Display" applications on the control panel always caused the control panel to close.

Now to confirm the original cause: I shut off, pulled the battery and put it back in, and my 770 wouldn't boot. 12 hours of fiddling later I've got it flashing, but it simply would not boot until, in desperation, I tried putting it in R&D mode. This time, the "Date and time" and "Display" applications worked normally. Then I switched off and tried taking it out of R&D mode (leaving the battery in), and it wouldn't boot. I put it back in R&D mode, and it booted.

I also noticed charging appears to be blocked in R&D mode. That was the final nail in the coffin, practically forcing me to conclude something is broken in the power management and charging circuitry.

I cross-posted to the maemo-users mailing list in hopes someone from Nokia would either (a) recognize the symptoms and say "oh yeah, that's a bad thus-and-such", or (b) not recognize the symptoms and want to know more. No response so far. Two cases isn't a trend, but it is interesting. I wonder if our units are from the same factory, have similar manufacturing dates, etc.