While attempting to assist Maintenance Control in investigating a de-icing boot anomaly after shutting down the aircraft at their destination; the Captain of a DHC-8 started the engine while the propeller tie down and the intake insert were still installed. The tie down line ended up snarled in the prop hub.

Narrative

While enroute we noted two items requiring AML write ups. The first was a [de-ice] Boot Advisory Light that was not coming on when the associated boot was activated. We were unable to visually verify if the boot was actually inflating. The second was the cabin pressure controller rate of climb was varying 1000 FPM up and down in the descent. Upon landing I contacted Maintenance and started the write up procedure while the rest of the crew completed their tasks and then went home for the night. While talking to Maintenance about the Boot Advisory Light; they asked if I could start an engine to determine if the boot was actually inflating. I advised the ramp that I needed to start the number 2 engine; they removed the cones and informed me that I was clear to start. The engine started and ran normally. It wasn't until after I shut down the engine that a Company ground Crewman brought me parts of the prop tie down. Apparently it had been left on during the engine start. After further discussions it was determined that the [intake] insert was not ingested but that the prop tie was wound tightly around the prop hub. Maintenance was advised of this complication and here I am writing this up.Factors contributing to the event included being the only person on the flight deck; being unable to see the engine before start; miscommunication with the ramp personnel; darkness and the lack of lighting on the ramp.