That would be incredibly hard on her system to be broody and so not eating much plus be molting. I'd make sure she had food in front of her on the nest or something. I spoil my one broody that way anyhow. She will just sit so long and won't stay off the nest long enough to eat what she needs, so I put a little cup of food and a cup of water she can reach from where she's sitting.
Oh and no, I never heard of one be molting and broody but I suppose it must happen.
Check her over for lice/mites, just on the off-chance that is the reason for her feather loss. If she has an infestation, that would account for her feather loss plus lethargy (which could be mistaken for broodiness). Hopefully that isn't the case though and if it is, it is easily treatable.
To give her a boost, mash up some boiled eggs (if she's moulting, the energy boost of the eggs will do her the world of good; if she's broody it will also boost her system).
Thanks for the replies! I'm sorry I missed them last week. I finally took her eggs away on Mon. Only 2 were developed and it looks like they stopped weeks ago. As soon as I took her eggs away, she was back out and about like normal. No mites or lice. She looks hideous, though!
sounds like ours are molting then! with few to no eggs, that makes sense!
we had really hot days for weeks, then really cold! I think they think it is fall!