LE front loader washing machine won't finish cycle?

So the not-that-old LG WM2050CW front loading washing machine won't work. We bought it 2.5 years ago. Warranty was for 2 years. In the past two weeks we've had several issues:
1. First it would stop at 13 minutes and spin slowly back and forth. Then it would stop and display a "UE" code. We looked up the code, decided to try redistributing the clothes, and got the same result. Several times.
2. So we called the repair guy. He came out and said it could be the floor (it's cement, but on one corner the floor dips as it heads toward the floor drain. We shimmed it up good and tight); then he said it could be the soap. Maybe too much soap in part of the machine. Then he said it could be a sensor. He didn't name the sensor, but did say it has magnets to balance the drum. He checked the sensor and it was bad. He replaced that and told us to run a cycle with vinegar and no clothes to clean it out. (He was a nice guy and didn't charge us as much as he could. I think he partly doesn't know what's going on either.)
3. We ran the cycle and afterwards managed to actually do a load of laundry, our first in at least a week. Hurray! Then we tried a second load and it stopped at 13 minutes and threw out a UE code. Called repair man back and he said we should move the clothes around. That didn't help, and in fact when we did another cleaning cycle with no clothes and some vinegar, the washing machine got down to nine minutes before it just slowly rotated back and forth, with several turns in one direction, and then several turns in another. This went on for several minutes but the display kept reading "9." I eventually unplugged it.
4. Today, my wife tried yet another cleaning round and it went past nine, and then a few moments later stopped completely and displayed a "LE" code.

We're at a total loss. What in the sam hill is going on with this thing? Could it possibly be dead already?

Matt M.
April 2013