If things get desperate, consult your local authorities. There are likely local ordinances regarding stray or unrestrained animals. Determine their recommendations and follow them. Be sure to treat all animals with kindness and respect, and always stay well within the laws of your community. I found a pigeon with a band.
Many folks breed and race pigeons.
These birds have private bands to identify them. To get an identification on the pigeon you found, try contacting a pigeon fancier's organization, or one of the organizations listed on the Pigeon Fanciers home page.