doesn't conduct electricity.
It does after a few days. Water has an affinity for carbon dioxide from the air and it will gradually collect enough to start conducting. Even "distlled water" has a pretty high conductivity, both from production and from sitting around in a bottle in storage. Distilled water is low in salts, but it's not particularly pure otherwise.
I don't suggest this as an electrolyte, but it's a real pain if you want genuinely pure water. You need to use deionised or reverse osmosis water, and for it to be fresh. You may also need to seal the surface of your experiment to keep lab atmosphere off it.