Washer will not go into spin cycle .Performs all other functions fine

If the individual part/function CAN work, but it wont complete a cycle, suspect the control board...

check function of solenoids may be worn cutterpin stuck in drain cycle

More than likely it has a broken wire underneath that controls the spin. and agitation. I had an old Kenmore that the wire that controls these functions would break about every 6 months.

The Service Manual for reference. Sears Parts Direct for reference.
I have tried to work with a few folks on this issue never received feed back to resolution see this post. I feel the issue is caused by one of three possible issues.

A stuck key issue/defective Spin Cycle key making constant contact forcing the Key/LED to cycle thru the Spin Cycle settings. Under normal conditions if you press and hold the Spin Select key it will cycle thru the settings, yours has a mind of its own (defective issue).

A false signal from the Control Board for the Spin Cycle.

A corrosion path issue at the Membrane Pad ribbon cable socket connection between pins 5 and 4. See page 20 of the SM button functionality “Spin” key.

Try to verify that the spin cycle membrane key is not stuck/defective signaling the Control Board to cycle thru the spin settings. I have not experienced this issue but let’s try the Membrane Pad Test to get a start point. See the Service Manual page 15, I have modified the process to make it a bit more understandable at least for me. Make sure the two digit display is not On or Lite.
Press the off button first so there is nothing displayed in the Two Digit display of your FAV6800AW.

Now Enter / Exit Service Mode

To enter Service Mode press the Enviro Plus and Spin Only keys for three seconds or until the control beeps. While in Service Mode, pressing the Presoak key will start a membrane switch check that verifies switch operation.

All the LEDs (except Presoak ) can be toggled or slewed by pressing the key associated with the LED or set of LEDs. Do not press the Presoak again during this test.

Press each key once and only once including the Signal Key the on side and the off side, also the UP and Down Arrow key of the LED display. All keys (including the OFF button) must be pressed within 5 minutes for this test to pass. “PA” will be displayed for five (5) seconds once all keys have been pressed and the test is completed (more like PA will be displayed for only a few seconds on my FAV6800AW). Following 10 seconds of inactivity at any point, this test will exit without any display. Let us know the results.

See my additional comment this board has message limit issues.

Replace the lid switch and clean out the drain pump.

rclasky check this one

http://www.fixya.com/support/t827165-maytag_model_lsg7806aae

did you check to see if there was anything stuck in the pump? sometimes socks and other small articles get dow there and wont allow the washer to spin or drain

Check your exit hose spigot, it may be clogged. This is if your filter is all clean. There should be air for passage in the standpipe behind. Your hose should not fit airtight into the standpipe and neither too deep into it. Snaking out your standpipe would be good too.

Rate me pl.....if helped.

service bulletin says the washer times can do that as the washer senses variables changing and all times are estimations and its normal .if the washer detects failure it will set a trouble code hope that helps