You need to take the cabinet off, pop the clips off holding the pump on, pop the clips then off holding the motor to the transmission and check the coupling. Unless you have the motor off you can't tell the coupling is good. Getting the cabinet off and on is the only hard part in all of this. The coupling itself is cheap and easy to replace, it connects one side of the motor to the transmission.
#13 in this diagram, part number PS1485646
http://www.partselect.com/Schematics...l/OUDZT8SQ.gif Whirlpool LXR7144EQ2 Parts List
This is a very common part to fail on these if you've been over loading the machine. It at first looks like a cheap design, but in reality its a well thought out life saver for you, cheaper to buy and replace this plastic coupling than the other option, burned up motor or transmission that could result from over loading.
If it was mine, I'd go ahead and just replace the pump and the coupling now while I had it apart, both parts are very cheap to buy.
Like I said already, you're tough part is going to be getting the cabinet off and on if you've never done it before or even seen it done. Since you have it laying on its back my guess is you haven't.
Stand it back up right, remove these #49 screws from each side of the control panel, and flip/pivot the control panel up and back...
http://www.partselect.com/Schematics...l/NZHCQY5N.gif
Now you need to pop these #6 clips out of the top with a flat blade screw driver...
http://www.partselect.com/Schematics...l/QY90HRUL.gif
Pivot the entire cabinet back then lift up, think of it as all one piece, the top, the sides and the front and pivot it back as if it were hinged down by the front near your toes. It will all come off as one big piece, You'll need to disconnect that #9 (lid switch) in the last drawing to remove it completely.
Back to this drawing...
http://www.partselect.com/Schematics...l/OUDZT8SQ.gif
The (2) #21 clips hold the pump to the motor, pry off the clips, don;t really need to remove the hoses, just force the pump with hoses attached out of your way.
Then pry the (2) #17 clips off the motor and pull the motor out from the transmission. The coupling which is likely your problem is in three pieces, #13 in that drawing. You're probably going to find either the holes on the middle piece are worn out, or the three tabs that stick out from the outer two pieces are broken off.
Push one part of the new coupling on the transmission till the center hole is flush to the shaft. Put the center piece on that portion of the coupling. Put the third outer part of the coupling on the motor and rotate it to line up with the holes on the center coupling piece. Hold the motor in tight with one hand and try to get your top motor clip on first (only because it will then hold the motor there while you force the bottom clip on making it easier).
Put your pump back on. Reconnect your lid switch, pivot the front bottom of the cabinet on first. Rotate it back to lock it into the rear panel (good luck, takes some doing), then force those top clips back in (good luck again).
If this coupling was bad, there will be no mistaking it, so no guess work required there.