I am so grateful for all the information that I found online, including this web site, that I would like to share the details of this repair in case it will help anyone else. Based on all I have read, getting these LG combo machines repaired by a professional service person can be nearly impossible, AND there is only one repair service anywhere near me that services LG and they have terrible reviews, so it was either fix it myself or have to buy a new machine. Ugh!! Pricey. So for about $60, a bunch of online research and some time--I fixed it on my own.
Based on the "bad" noise before the machine attempted to drain, I suspected I needed a new drain pump. Before I ordered the part I dismantled the machine and looked for clogs, however. I followed these excellent instructions (http://fish.freeshell.org/LGWM3431HW.html) to get into the top of the machine. While I was in there, I cleaned a bunch of gunk/lint out of the dry duct and the condensing duct (as is recommended by users of these machines, even though LG does not tell you to do this).
Note: It appears impossible to remove the condensing duct to clean it out completely without taking apart the entire machine, so perhaps don't bother trying. I stuck a dryer-duct cleaning brush down in there from the top and cleaned out all the gunk I could.
Next, with the help of some "generic" videos on replacing the drain pump on an LG washer (https://www.youtube.com/watch?v=8cPl22OC9f4&spfreload=10, https://www.youtube.com/watch?v=8WBTgGSFeQs&spfreload=10) and a Service Manual for the WM3431 that I found online for free (after a long search; I would post the link but I lost it), I removed the front of the machine to access the drain pump. This involved: 1) removing the top "control" panel (but not disconnecting it); 2) unscrewing the door lock; 3) releasing the door seal; 4) removing the front "door" panel (and disconnecting the door lock wires so to move the panel completely out of the way); 5) removing the lower front "coin catch"/drain panel. Details of all this are in the videos.
Once the machine was dismantled I could access the drain pump. Disconnecting the drain pump involved: 1) unclamping from the drain pump a large black hose that runs to the washing drum; 2) unclamping from the drain pump a smaller gray hose (the drain hose); 3) releasing a tab underneath the pump, allowing it to slide back and out; 4) releasing (by pulling out) two wire connections at the back of the pump. Then I checked the gray drain hose and the black hose for clogs. There were none.
Once the drain pump apparatus was out of the machine, I removed the drain pump from its housing by releasing the two side tabs and unscrewing two screws.
I replaced the drain pump motor and the plug that closes the coin catch (like a gas tank cap on a car). I would have replaced the drain pump housing as well, but that part is not available for purchase. I put it all back together by just doing everything in reverse.
Note: The WM3431 is NOT a machine that is easily accessed through the bottom, unlike many other LG washers. I tried that. After unscrewing MANY screws and trying to pry the bottom off, I discovered that it is constructed from the bottom up, making the bottom impossible (?) to remove. I gave up at this point.
Another note: Reinstalling the wire/spring ring that holds the door seal in place is really not that bad. I did it solo (twice!), using a variety of kitchen utensils (butter knives and the handles of measuring spoons). If you have ever put a racing tire on the rim of a road bike, you'll figure out quickly how to work with the wire/spring.
I have run the machine through a Rinse/Spin cycle, a Wash (but not dry) cycle, and a full Sanitary Wash + Dry cycle so far with the new drain pump. It appears to be working beautifully. And the clothes are coming out of the dryer scalding hot again. Previous to cleaning the dry and condensing ducts, the drying performance of my machine has declined noticeably.