Product review (5 stars): LG Washer WM2077CW fixed for $16.50 !!
If your LG washer won't spin or showing you a "LE" error every time after you start a wash cycle, this is the first thing you should try.  It's cheap and takes about an hour to finish the whole project.  Following youtube video will show you how the washer behaves when the hall sensor needs to be replaced.

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And this youtube video will show you how to replace the hall sensor.

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You can also download the LG washer service manual from the link below.  It has additional troubleshooting steps.

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Remember, other parts failure also causes similar problem.  Here is another video which shows you a different part failure causing similar problem and how to troubleshoot and fix the problem.

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Try this and save yourself a lot of money!