What is your definition of "do not conduct electricity"?  Do you have a specific electrical conductivity value in mind?  Metals have a wide range of electrical conductivity values, but I do not think you will find what you want.  By definition, metals have metallic bonds, which have delocalized electrons that are available for conduction.

I agree with Corypad. I always thought that one of the defining characteristics of a metal was it's ability to conduct electricity.

When an element has an energy gap in its electron structure, like silicon, it's still technically a metal but doesn't conduct current at all voltages; only when there's enough voltage to overcome that energy gap and elevate electrons to metallic conductivity.
 That's as close as you can come to a non-conducting metal.

...which is why silicon, gallium arsenide, etc. that are used for microchips are called semiconductors.

Trying to decipher the originator's desire, why use a metal?  Metals are deformable, but silicon is not.  Therefore, silicon does not share the usual properties of metals, and should be considered as a different class.  In elementary school, we were taught that they were metalloids, but this term seems to have fallen into disfavor.