According to NEWTON, ice can conduct electricity, but it's a very poor conductor. Water doesn't conduct electricity; impurities in the water (ions) do, and ions don't tunnel around very quickly in frozen water.
Pure water does not conduct electricity, and so a block of ice frozen from pure water would not conduct electricity at all. When water conducts electricity it is actually the ions (charged molecules or atoms) dissolved in the water that are the cause. These ions allow for conduction. In liquid water, these ions are mobile, allowing for conduction, but because ice is a solid any ions present are not mobile, making ice a very poor conductor.