If you don't have access to one of the rescue centres listed or they can't take your rescue then these are good places to look for advice, support and help:
Pigeon Protection and Rescue (UK)
Pigeon Angels (International)
Pigeon and Dove Rescue (International)
If you have a sick or injured pigeon please do not feed it immediately, it may be suffering from shock and/or dehydration.
If it feels cold it is important to warm it up on a hot water bottle wrapped in a towel so it is warm but not hot) or on a heat pad set low, or under a 40 watt angled lamp for about an hour. If the pigeon is wet and hypothermic you can use a hair dryer but make certain that the air reaching the pigeons is not too hot.
After the pigeon has been warmed (that will take about an hour) mix 1 pint warm water with 1/2 tablespoon of glucose, or honey or sugar and half a teaspoon of salt. Dip the bird's beak in the warm water to encourage it to drink, but don't try squirting the water into the birds mouth as it might aspirate.
Do not try to feed the bird yet. It might not be well enough to digest the food, which could kill it. The glucose/honey/sugar will provide the energy it needs for the moment.
You should also check the inside of its mouth which should be clean and pink and pop a clean white kitchen towel under it so that you can monitor its poops.