1999 Ford Puma Starting Problem.

Hi, Im Having A huge problem with my Ford Puma. 1 year now suddenly stops starting. I bring it to the garage they change the start motor (battery is fine) I paid 400 euro the firt time. After that works 1 week then again same problem last 4 months worked only for 2 to 3 days. I start it always with a little pushing. It needs very little I even do it by my self, the garage 10 times dont take money from me cause I paid the first time and they vcannot really tel me whats the problem. I notice that sometimes it works and mostly when is cold and wet outside I dont know if that have something to do with it. They told me to check my earth wires, Can you please help me I am desperate for an answer since I have a little baby and a woman with cancer and is necesary my card to start, thank you Manos