You need to observe the agitation to see if perhaps it's not oscillating properly, which may indicate a problem with the transmission.

The trick is that if the machine won't run / agitate with the lid open, you have to either trick the lid switch or temporarily bypass it with a jumper wire. The switch on your model is hidden beneath the top and triggered by the left-side lid hinge. A way to trick it is remove the two hinge screws at the left edge of the lid, pull the hinge arm slightly out of the lid and rotate it down to trigger the switch. There should be a position somewhere on the timer to make the machine agitate without water (post a pic of the timer if you need help finding it), or you can run it on a low fill level.

Another possibility is a problem with the "dogs" that engage the upper spiral/auger section. Does it turn freely both directions? It should spin freely clockwise without rotating the lower fins. Counterclockwise the dogs should engage and the lower fins should turn with it. Rotate it back and forth repeatedly to make sure the dogs grab consistently, sometimes they're broken in a way that some positions they grab and some positions they slip.

Thanks! I will check when I get home tonight/tomorrow. I have noticed that clothes seem to be getting wrapped/tangled around the agitator since the noise started. Not sure of that means anything or not.

Wrapped clothes may be caused by the agitator (base part/fins, not the upper auger) rotating around continuously in one direction instead of oscillating ... broken gear or other problem in the transmission.

I checked the washer this morning and the upper agitator spins freely in both directions (it seems kind of loose). I also rigged the machine so I could observe the agitator in the "agitation mode" with the door open. The bottom portion of the agitator is spinning counterclockwise quickly while the top portion is loose (I can hold it in my hand with no resistance while the bottom portion rotates). What should I order?

Base of the agitator spinning continuously one direction indicates the transmission is bad. That's the cause of the clothes wrapping and the unhealthy noise. Fix is replace the transmission. Part Number 3360629. Cost between $112 and $168-ish + shipping depending on the source (online prices for DIYer. There are also many choices on eBay ranging from used to open-box to new. Replacing it is not difficult for an experienced DIYer, there are how-to videos on YouTube. A servicer will of course cost more. It's worth doing the repair if the machine is otherwise in good condition without excessive rusting and other wear-and-tear. Whirlpool stopped producing this washer design approx 2010 and there's nothing on the market that compares to it for reliability except maybe Speed Queen.

The top auger also has broken dogs, which is a separate problem from the transmission. The dogs are a couple dollars. Or there's an agitator repair kit (few dollars more) that includes some other items. You'd need to disassemble the agitator to check if only the dogs are bad or if the other parts are also needed.
Agitator Dogs = Part Number 80040
Agitator Repair Kit = Part Number 285809
(note to others reading this thread, there are three different agitator repair kits for tall, medium, and short cam agitators, they're not interchangeable)