Read the advice here from @bdum and several others and added a 47uF 16V eBay tantalum capacitor in parallel with the existing one on C102. Now, my old LN40a550 fires up immediately. The retirees I'd given it to were leaving it on 24/7 to keep it from turning green/screaming because it's their only form of entertainment, and iirc the TV is rated at 200W.
I didn't do any scraping, just soldered positive to positive and negative to the big ol' hemispherical chunk emerging from the PCB nearby as suggested on the forum. I have one new capacitor from my purchase remaining in case I need to add it to C131 on the other side.
I read this thread through at least twice, so thank you to all that posted before me.

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