Cell phones would go down because the cell network relies on land based towers... which rely on land based power and fiber optic lines.

Without the technicians that maintain the system, power plants would be the first ones that would shut down. Failsafes are in place to prevent damage should humans leave the picture.

Some cell tower sites have a back-up generator. However the fuel would only last a day or two at the most.

Secondly, without the technicians that maintain them, the vast network of land based lines that connect the towers would fall into disrepair.

It would only be a matter of time.