PA-28 pilot reported ice on the parking ramp during a fuel stop. After engine start for departure; the aircraft began to slide on the icy ramp surface with the parking brake still set. The aircraft slid into a taxi sign and taxi light before the pilot noticed; damaging the propeller and engine cowl.

Narrative

At approximately XA00 on Day 0 I departed ZZZ1 operating a PA28-181 flying direct day VFR to ZZZ; and landed at approximately XA25. I parked on the western portion of the ramp and set the parking brake. At the time the temperatures were above freezing with some partial sun and the ramp had some thin patchy snow that was melting and wet; and I had parked in a mostly wet area.I ate at the restaurant while the plane was refueled and went back to the plane after dinner. It was dark; the runway and taxi lights were not on; and the western section of the ramp had no illumination. At XC03; after a normal pre-flight inspection by flashlight; I started the aircraft normally and idled at 1000 RPM while starting to look at my checklist and getting ready to click up the taxi/runway lights. I had a cockpit light on. The parking brake remained on. I did not perceive; while looking at the checklist and bringing up the avionics switches; that the plane had begun to slide; move forward; and pick up momentum on a significant patch of ice that had formed as temperatures dropped below freezing. As the aircraft crossed into a dry area of the pavement; I heard an unusual sound that I immediately but incorrectly assumed to be an engine anomaly. I quickly pulled the mixture into an off position but nearly simultaneously heard the prop make contact with an unlighted runway sign and a nearly co-located unilluminated taxi light. The aircraft came to a stop a short distance from the ramp edge.The aircraft sustained propeller damage. The cowling had some very minor damage. There were no personal injuries.