Lethargy in myhen

[Sambin064]

I have a 8 month old hen that I found still on her perch. She even let me pick her up and examine her. (Unusual)
She drops head.
My Roosters comb has patches missing close to his head.Is this a problem.

 

[Eggcessive]

Is her tail up or in the down position? I would take her aside, and get her drinking some water with electrolytes or sugar water. Offer some scrambled egg bits. Wet chicken feed is also good. Feel of her crop to see if it is empty before feeding her. Is her vent dirty? What do poops look like? Does she lay eggs?

A picture of the comb on your rooster would be helpful. Do you have other roosters?