Originally Posted by moonscape
1. Are power supplies and caps separate issues?
No. Each power board has a number of large-ish vertically mounted cylindrical caps. Some times when they go bad, the top end bulges, which is easy to notice; other times, there is no visible symptom.
2. There is a local electronics shop where I can have the caps replaced. Is there just one board (power?) to be removed and is it easily accessible?
No. There are two power boards; the main-smps (switch-mode-power-supply), p/n BP44-01001A, which is located above the main board's metal cage (on the left side, looking from the rear), just to the right of the input jack panel; the other is the sub-smps (p/n BP96-01726B), which is located on the right side, above the LED assy, and has a slanted edge.
First thing is to remove the 10 screws holding the lower back cover, then everything is accessable. These boards are not difficult to replace, noting that sometimes the wiring connectors can be a bitch to disconnect without tools. While you're at it, vacuum out the dust.
3. Would it be easier to just get a board on eBay, and what exactly would I be searching for?
The board part numbers are mentioned above. At any given time, they may (or may not) be available on ebay or other TV parts sites. Ask your local shop whether they can test boards for this model TV, and what it would cost to replace the electrolytic caps. I typically replace the caps myself in a case like this, but I have 30+ years experience in desoldering/soldering and electronics.