my seiko kinetic watch has stopped?

The capacitor cell has exhausted, they only have a life of about 5 years. It needs upgrading to one of the newer titanium lithium ones. You can do it yourself provided you have good vision and dexterity. Your watch might also need cleaning but you can try swapping the cell first and see if it's OK.

Step by step photo guide is here with links etc.
http://www.epemag.net/replace-seiko-kinetic-cell.html

Lurkio
July 2010

It may need a replacement for the capacitor - Seiko issued replacement parts (a LiIon cell) for the capacitors originally installed in many older Seiko Kinetic watches. The Seiko replacement kit can be had for under $20, and the replacement is not extremely difficult.
Here's a site describing how to do it:
http://www.alexanderscott.com/seiko%20repair/seiko.html
And here's a site that sells the replacement parts:
http://www.swatchbattery.com/

To figure out which replacement part you need, you'll have to identify the movement # of your watch - it's the first 4 characters of the eight character string printed on the back of the watch - Mine was a 5M42.

And there are several jewlers who will do the repair for you if you prefer not to open your own watch and fiddle with hardware the size of gnat droppings.

Bill
October 2008