I repaired my clock myself, assuming you have followed the above instrcutioins to get the clock out you can test to see if it is a simple fix or a more complex one.
There are 2 simple fixes.
1. - It needs cleaning and oiling (use watch oil as it is much finer than 3 in 1 or similar)
2. - the fuse has blown (see here...
http://www.sl113.org/wiki/Electrical/Clock)
To identify the fault you need to strip the clock down, the fuse issue can oftem be seen by naked eye, but the "cleaning" issue is less obvious. The clock is "electro-mechanical" this means that it uses asmall current from the battery to "re-wind" the clock once every minute or so. Careful inspection of the mechanics should identify the winding flywheel (sorry no pictures), gently wind the clock manually and check if the clock begins to tick (the movement starts to move). You may find it starts and then stops straight away, if this is the case then it is almost definately dirt and dust.
Now this next bit goes against everything you will want to do, but trust me its OK. Fill a bowl deep enough to cover the mechanism in warm water (no soap). Then emerse the mechanism only (not the clock face) into the water and agitate it for a few minutes. This will losen any dust blocking the mechanism and wash the interior of the clock. When you are happy that you have cleaned it, leave the clock in a warm dry place to dry out. I left mine for 48 hours. Once dry, using clock oil, oil as many of the pivot points as you can. My clock oil came with a needle aplicator which helps to get to the awkward parts. When you are sure that you have oiled everything try winding the clock again...good luck, it should now work.
I cleaned mine about 12 months ago and it is still working now...although I am told that timekeeping is not something that these clocks do well, depending on how humid it is mine will lose or gain time.
Good Luck.
M