I don't blame you for being worried - there's something wrong with this youngster as ALL birds are pretty fastidious about not standing in or nesting in their own droppings.
Even tiny chicks in the nest will instinctively back up, lift their tails and aim a dropping over & out of the nest or at least out of the area they're sitting/standing in.
When it comes to pigeons these days, I'm afraid there are too many diseases to mention that this one might have (or at least be a carrier of). I'd get the bird to a wildlife rehabilitator (call them, usually they'll make house calls to remove the animal).
If this bird can be treated and saved, they'll likely do so and re-release it; if it can't be saved, at least you'll know it had a humane euthanization and did not suffer.
Though it might not look like its in pain or suffering, not moving and standing in feces is not the kind of life this bird is meant to live or comfortable with.
Here's a search engine to start with:
http://www.tc.umn.edu/~devo0028/contactA.htm
Also, call your local Humane Society for a list of numbers that might be helpful and of course your city or county animal control offices.
And thank you for caring enough about this little bird to want to help!
Certified Avian Specialist
Cert. Avian Specialist; Int. Assoc.Animal Behavior Consult; Pet Ind. Joint Advisory Council; author