I assume that you have a top loading machine. Before you do anything try the cycle again. Since it is full of water it probably wont fill up much more with water. Make sure your machine starts the agitating, if it normally happens here. No agitation = bad motor or belt = pump not working. Or bad timer.
You should listen to see if you hear the timer click to indicate a new part of the cycle. If it agitates then your timer is probably OK but I would listen for the click to signify the spinning and the water to pump out. If it spins then it is probably the pump. Motors reverse for the spin cycle (or 30 years ago they did). No spinning could be bad motor or belt. Pump won't work if motor is not turning.
The next thing I would do is drain all that water out with a coffee can or something big, unless you have a siphon. When you get all the water out there is still more, you've only emptied the inner tub so the washer will still be heavier, but probably manageable. Now follow the other answers, they are all good and unhook your machine. KEEP YOUR DRAIN HOSE ABOVE THE MACHINE AND DO NOT REMOVE IT.
Check your belts to see if they are still snug or missing. This can be a problem. It could also be something like a sock in your pump or your pump has gone bad. Inspect the pump and carefully pull the drain hose from it. It will leak that cruddy water I talked about earlier.
I haven't worked on machines in close to 30 years, when I worked for Maytag, so some or all might this might be outdated.
EDIT My front loading has a small drain pump filter behind a little door in the front of it. See if cleaning this will help. You might check out the manual or look it up on line to give you tips about this. Make sure you have something for the water to drain into while you do this. I don't think this will drain all water, just the water between the pump and the dump hose. Maybe this will help. Thanks @BMitch
The way we move them after emptied out was to get a good grip on the washer and tilt it forward with your knees against the front and lean it back until it is barely off the floor and your knees taking the weight. Then you just slide yourself backwards until its out. Since you have a counter to dill with try getting a handtruck, slide it in the middle bottom and pick it up until you can pull the handtruck and the washer at the same time, using the bade and the bottom of the machine.