At Ben’s recommendation, instead of taking it to Apple, I took the Mac into a local, highly-recommended shop today.
Worst case scenario is the system board. $900 including labor. (Better than what I was reading about Apple.)
Best case, $50 to simply clean the thing out.
The tech told me it might also be a simple matter of the power button being hosed. If that’s the case, it’s an upper case/keyboard replacement (because both items are apparently sealed to each other) at around $300, including labor. (The fact the charging light came on was a good indication the system board wasn’t fried.)
Should hear something from them within 24 hours.
UPDATE: Worse than Worst Case. Pretty much everything except the display is shot and needs replacement. Time to buy a new Mac.
At least Gazelle is giving me $185 to offset the cost of a new one a bit…