Thanks for all the answers, everyone. Unfortunately, I'm not an engineer, so all I know from previous experience and reading about other people's problems with their TVs with similar issues is that failing capacitors is a likely culprit. I
am good with a soldering iron, so my plan was to just take a shotgun approach and replace all of the capacitors and hope for the best, which is what I did with my own TV that was having power issues. I was hoping that when I looked at the capacitors that I would find at least a few that were bulging/leaking/etc for obvious visual confirmation that they were done, but all of them are visually intact.
BTW does it not power on at all? Did you check fuses, voltages. My gut feeling tells there is nothing wrong with capacitors in this case.
According to my friend, the TV will sporadically turn on. I'm not sure how often it will actually turn on, but he says he just tries to keep turning it on over and over again until it finally does turn on. Once it does turn on, he claims that it will stay on indefinitely.
When it doesn't turn on, the TV will still initially react to the press of the power button by briefly turning off the red power LED, but then after a few seconds, the power LED will change back to red to indicate that it's in the off state again. Unfortunately, like I mentioned above, testing things like fuses, voltages, etc, is beyond my limited knowledge.