I bought a new video card yesterday. I hadn't planned on doing so, but when your old card dies, it's time for a new one.
I didn't know right away that the video card was the problem, but it was a pretty high-percentage guess. That earlier flickering screen was a giveaway, as well as the fact that I could see keyboard and case lights come on when attempting a reboot. Motherboard or power problems would likely not show any lights at all, and drive- or memory-related issues should show something on the screen (even if only an error). Just to be sure, I broke out an old video card (from several years ago before my last upgrade) and tried it out. That worked, confirming that the video card was the issue.
The card that just died was a NVidia GeForce GTX 650 Ti Boost. It's just over three years old, which is pretty ancient in terms of computing technology. I hadn't had any complaints in terms of performance, and three years is pretty decent in terms of life of a video card that's used regularly on a gaming machine. Using that old card wasn't an option - way too underpowered, which is why it had been replaced in the first place - so I needed a new one. I figured my best bet was to go with a similar card in hopes of the same kind of lifespan and performance.
The 650 is way out of date now, but NVidia makes a GeForce GTX 1050 Ti that's basically a later version of the same thing. I poked around on various shopping sites and found that it was pretty affordable, around $160. That's right in the sweet spot for gaming video cards, at least in my opinion. A bit more than the super-cheap cards with short lives and/or bad performance due to cheap manufacturing, and a lot less than the high-end cards that provide way more power than necessary for my needs.
I do a lot of shopping online, but when I want something quickly it's nice to have local stores. Best Buy had the card I wanted for basically the same price as I could get at online retailers, and they have a store about 15 minutes away. I used their in-store pickup option to place the order, and drove up to pick it up about an hour later.
Back in the day, installing a new video card was a major pain, but these days it's a pretty painless process. Honestly, the hardest part was lining up the screws to hold the card in place against the back of my case. Even driver installation was no trouble, just a quick download from the NVidia site. I did make sure to choose the clean install option so it would remove the old drivers, just in case, but even that was likely unnecessary.
Everything I've done on the computer in the last day or so has worked fine, so I believe the new card has settled in nicely. With luck, it'll be another three years before I have to worry about it again.