Baby pigeon or dove, legs not functioning, paralysed, limp, metabolic bone disease
Baby pigeons and doves (specially wood pigeons and collared doves) that have a calcium and vitamin D3 deficiency will be unable to use their legs, sometimes the legs will trail behind them as they try to use their wings to drag themselves along. Other common symptoms of this condition are a “rubbery” beak and feathers that delay in coming out of their sheaths, so that they look like little “tufts” at the top of a stalk.
Case history : Doveling
When this little dove was found her legs were completely limp and she was dragging them behind her as she pulled herself along with her wings. I placed her legs in the right position using the same method that I used for 
Gonzo. then I made little tubes of self adhesive bandage, placed her feet around the tubes as if she was perching and taped them into place with more self adhesive bandage. When working with doves it is important to work slowly and gently and to watch out for signs of stress (eg open beaked breathing) because they can die of a heart attack if they are stressed. As soon as the bird shows any signs of stress stop working on it and leave it alone and quiet.
I gave Doveling Calcivet and access to natural sunlight. The tremendous improvement in the state of her legs is apparent in this video, Doveling is in the foreground.
Sometimes when a baby pigeon is nesting its leg will slide out from under it and grow pointing out at the wrong angle. This can be corrected if caught early enough. For advice on how to prevent a nestling in your care from developing splay legs please refer to the page on bedding and housing for a baby pigeon.
Case history : Gonzo
When I first saw Gonzo in 2004 she had already fledged and was feeding with a flock of pigeons in a grassy area in the city centre. One leg stuck out at almost a right angle to her body, 
she also had a hooked beak that made it difficult to pick up seed, but this gallant little bird showed no self pity and joined in the flock's formation flight overhead, distinctive even from the ground because of her deformity.
Despite her brave and positive attitude, her life expectancy was even lower than normal...90% of fledglings die within their first year of life and as her beak would soon make picking seed up impossible which would lead to starvation, so I took her home.
I didn't think that it would be possible to fix a splayed leg that late in her development - she must have been at least 6 weeks old. Fortunately an experienced American rehabber called Marian Isaacs, who was a member of a forum that I consulted advised me that correction was still possible.
Marian recommended moving the legs back to their natural position and binding them there for a few weeks. 
I found out that when I moved the splay leg inwards, Gonzo was able to stand straight and normal, so I linked the legs with a length of Boots self adhesive bandage to hold the splay leg in but pressing the bandage between her legs together to avoid to leg being pulled too far towards the other. To my surprise, with this bandage support Gonzo was able to walk properly, fly and even perch!
As splay legs can be associated with a calcium deficiency I gave her supplements of Zolcal D.
I kept the bandages on for three weeks, removing them occasionally for a few minutes to see if the legs would hold: it did. She was able to walk and perch normally, lay and sit on eggs and have a normal, though sheltered, pigeon existence.
Gonzo grew up to be an odd little hen. She is much smaller than the others and her head is particularly small which makes her eyes look larger than usual. Her mate is one of the biggest cocks in the aviary, a handsome white pigeon so they make an odd couple. Her legs are a bit stiff now, so she walks with a bit of a waddle, but is significantly better that when I found her although
her beak grows into a hook very quickly and needs regular trimming .
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Sometimes pigeons will lose the lower part of one - or even both legs - to string damage and and walk on a stumps. Sometimes the whole leg is smashed and has to be amputated by a vet. These pigeons are able to live happy healthy lives and have even been known to survive in the wild, and to have mates.