After being covered in snow for a week I went outside yesterday to clean off and start my '02 XJ Sport. It was on briefly (a few seconds) though, from the last time I was in the car, and I turned it off immediatly (I know better then to try the wipers when there is a bunch of ice and snow on it.). It did not move because it was froze to the window. So I cleaned off the window, freed the iced over wiper and tried to clean out the channel of the thick ice that had built up over the last week. When I turned on the wiper, it unfortunatly only worked briefly...maybe moving only a few inches. I tightened the nut about four months ago when it got loose, so that is not the problem. When I bought the car last May the wipers would not work at all....it was a bad relay...it was fixed, and has worked fine ever since. If I turn off the wipers for a minute and turn it back on it may respond for a few inches but stops and will not progress.
So, does anyone have any idea what it could be?? Do you think I broke the motor assmebly somehow?

 

When this happened to me last year after the car had been buried for a few days it was due to ice buildup under the cowl cover. I let it run with the defroster on high until it thawed. It took some time. Hope that's all it is in your case.
Bob