First, test the GFCI properly
I am always cautious when people replace GFCIs. GFCIs are very poorly understood, and I find 90% of the time they are "throwing parts at a problem". This is a waste of money, and invites mistakes.
So let's make the relevant test. Remove the wires from the LOAD terminals. (you have to loosen the screws to do that; these are screw-and-clamp. Then cap off the wires.
Test the GFCI now. Does it clear? I bet it does.
So now you need to search for which outlets and loads have lost power. One of them has a problem, specifically a ground fault, You'll need to reattach the LOAD wires, then eliminate loads one at a time until the problem clears. If removing all loads doesn't clear the problem, then it's in the wiring.
It's unlikely to be the GFCI.
What is LOAD?
It is my understanding that the line wires are the power source coming to the GFCI, and the load wires are providing power to the next receptacle (or switch, etc).
No. That's not what LOAD means at all. What you're referring to is "onward power" and just gets a plain splice.
LOAD means "the downline devices subject to control from this device". GFCI is a ... well, you don't know what it is. When you fully understand GFCI, you can can put it to use. That will come in time, but recognize it isn't now.
In the meantime, don't use it. Or in this case, don't tamper with it.
Leave it exactly the way you found it.
Does anyone know why there is 4 line wires? The instructions on the new GFCI explicitly stated not to use if more than 4 total wires (e.g., 2 line, 2 load) not including the ground.
What that is saying is that >4 wires is beyond the scope of the DIY instructions. What's the story there? Your GFCI device has a UL listing. A UL listing doesn't just approve the device bare, but the device, labeling and instructions as a matched set. (that's why instructions can seem so dated and horrible; companies are reluctant to update them because they don't want to mess with their UL listing).
Instructions to include various 6-wire iterations would be much more complicated, and involve more haggling and uncertainty about the UL listing being approved. So "Ask your electrician" was the easy way to do it.
For you, it's simple enough. If you have 2 wires that definitely land on the same terminal and are definitely connected, those can be replaced with a pigtail. Doing so with the LINE wires reduces your wire count to 4, and makes the instructions followable.