The complete model number looks to be 106.59592990 making it a Whirlpool built model.
** I put a screwdriver behind the panel and I tried to pop it off, but it didn't seem to want to release **
You can see an exploded view diagram of your dispenser mechanism at the following link:
- Kenmore 106.59592990 Water Dispenser
LINK >
http://tinyurl.com/9crqx
On some models the front dispenser cover (drawing item # 23) will peel off. The housing mounting screws may then be able to be accessed, if necessary. You can see the lever activation switches (drawing item # 14) at the link below.
- Dispenser Lever Switches (4)
LINK >
http://www.appliance411.com/data.php?rc=445177
JFYI
Dan O.
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