Mystery rattle and Mystery part... are they related?

Ok, so this is a new-to-me 2006 and I noticed an audible rattle upon moderate acceleration, most noticeable around 40mph.

It seems like the engine is vibrating at a particular frequency, which is subsequently vibrating the object... That's my best guess.

The previous owner's son showed me a part that he could not figure out how to reinstall after he finished replacing the rack and pinion in the steering shaft.. its a rubber thing. It seems to be missing from the area where the rattling is coming from... Could they be related?
I've included an audio file of the noise and a photo of the part..


Rattle Noise.m4a

Context: I've been noticing lots of broken/missing plastic clips, zip-ties, and random bolts used to fasten things down, so the rattle may very well be a loose bolt that was not reinstalled. I'm hoping thats all it is.

 

For those who can't listen to the audio file.
It sounds like a very thin aluminum can filled with about 4 erratic carbon fiber butterflies.
It sounds like a plastic spork dancing in a garbage disposal.
It sounds like 10,000 staples are being sprayed at you with a modified leaf-blower, and all you have to defend yourself is a shield of clear plastic.

 

The cigarette lighter pictured was not found in the car.. The one I found in the car was empty. I found about 100 business cards, various petrified food items, hairclips, old makeup, melted candy, and several milkshake/frappuccino stains

 

So, would you suggest taking it to a dealership and explaining the situation? I wonder how much they'd charge to check it and reinstall the part.. The part is kind of rusty -- maybe I should clean it before reinstall?