Taking care of a baby pigeon

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We've found a baby pigeon in our yard. It seems it fell off our or our neighbor's rooftop from a nest. It's impossible to go up and put it back or something like that. So we're keeping it in the house, in a rather large cage, and sometimes we let him free in the room. He can somewhat fly, short distances only. We gave him water, grain, bread and soaked bread (in case he won't eat solid food). However, he doesn't seem to eat. It's probable that he was still fed by his mother and he's not used to perform the actual act of eating, so we've been hand-feeding it successfully. Do you have any advice about taking care of it, what food it should be given, when will it start eating on its own? We're not really sure what to do with it either, and we can't afford expensive veterinarian treatment.