About the best thing you could do would be to get someone to donate their services with a backhoe, dig a trench and install some stone and drain tile in the areas you speak of.
When it rains the water will filter down through the soil, through the stone and into the drain tile which will carry it away from the area that now floods.
The materials are not that costly, the biggest expense is the backhoe so work hard to get that donated.
Good luck.
CV