Washer fills, agitates but won't empty or spin

I read through all the links but still can't isolate my problem. I have a Whirlpool Model LA 7680XK which I bought used a few years back. As a handywoman I have made many appliance repairs myself. Amazing how simple some fixes are is you know how to approach it.
As I said in the subject line, the washer will fill and agitate but even when I move the timer through the cycles it will not empty or spin despite the fact that the motor is running.
I lowered the drain hose close to the floor and the water immediately ran out. I then tried again to get the washer to spin by putting the timer near the spin cycle and waiting. It tick, tick, ticked (timer working ok?) but it continued to the stop position without spinning.
My washer normally continues to agitate when the lid is up so I don't know if the problem has to do with the lid switch but it makes a clicking noise when depressed so I don't think that this is the problem.
I noted that when I put the load in that the piece of wood that I had under one corner to balance it out had slipped out of place. No doubt my last load was seriously unbalanced. Thought I might note this since I suppose the jarring could also cause problems.
I fear from reading posts that I will have to replace the pump but before going any further I wanted to make sure that there weren't any other options.
Thanks in advance for any assistance. I sure love the fact that I can go online and get information.
JayLene - handywoman by necessity
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I'd suspect a blocked (or partially blocked) drain system in the machine and/or a blockage in the level sensing system.
The latter works by having a level sensor (2.5" dia. disk, a couple of wires, and a thin, usually clear pipe to the drain system). If there is a blockage, it thinks the machine is still full and prevents spinning etc. Sometimes leaving the machine allows the pressure to equalise and the program will continue.
Chances are it is all gunged up with a grey paste - a mix of detergent, bodyfat, and muck. Yuk.
--
Brian Reay
www.g8osn.org.uk
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