So, I think I have determined that the problem is with my monitor and not with my video card.
Yes you did - perfectly. You proved your card and computer work by trying another monitor. You eliminated the cables by trying a different set, which, in turn, ensured a connection was not simply loose. And you proved there's a problem with the monitor by trying it on another computer.
I'm wondering if anybody has any ideas about why this happened or what I might do to fix it if anything or what I might do in the future to prevent this sort of problem.
Without knowing the specific component that failed, and its function or circuit it supports, there's no way to know the real reason why this happened.
LG makes good monitors - but they make millions of them. So what are the odds, a million to one you got a lemon? It happens. Like most any electronics device, a monitor is assembled with 100s of components from many suppliers. LG makes a million monitors, but might use 10 million of one type capacitor in them. Even if only .001% fail (a remarkable, and probably impossible manufacturing accomplishment, BTW), that's still 10,000 potential failures. And until Man can create perfection, there will always be some flaws.
So why did it happen? Bad luck or some outside influence.
Typical suspects? The monitor's power supply. The backlight. The inverter. If you try the monitor again, shine a flashlight at the screen and see if you don't see a very faint image. If you do, the backlight or inverter are suspect and these can be replaced, typically less than $150 for parts, and 1 hour labor. If you see nothing with the flashlight, then it's something else, perhaps the power supply.
If the problem is simply a part that failed prematurely on its own, there's nothing you could have done to prevent it, or to avoid it happening again. If some outside influence caused it to fail, maybe you can prevent recurrance. I am assuming it was not dropped or banged about, or had liquids spilled inside. So that leaves the food supply - power.
All computers should be on an UPS
with AVR (automatic voltage regulation). An 1000VA UPS
with AVR will easily protect a typical computer, router, modem, and two! LCD monitors from surges, spikes, sags (opposite of surges) and dips or dropouts (opposite of spikes). EVERY
time the microwave oven, refrigerator, hair dryer, toaster, coffee pot, air conditioner, water cooler - any high wattage device- cycles on and off, anomalies are sent down the line. A surge and spike protector is little more than a fancy, and expensive extension cord that does NOTHING for low voltage events, or long duration surges. These anomalies are constantly banging on the power supplies and regulator circuits in electronic devices. They are designed to handle "normal" events (whatever that means) but in doing so, they work, and generate heat, which causes all electronics to "age".
If you have any high wattage devices in your home (who doesn't?), office, or apartment building, you need an UPS
with AVR to protect your computing assets.
with AVR takes the abuse and feeds your valuable electronics good clean stable power. It tames surges and spikes, and uses its internal batteries to boost sags and dips. Power backup during a power outage is only the icing on the cake - it's the regulated voltage that's really important. So, to help
prevent premature failure, use an UPS
In the meantime, LG monitors typically have a 3 year parts and labor warranty. Contacting LG is your next step.