Need Help !!

Well my car has had problems starting when its cold.It takes me about 2 times to get it started.Well today I was going up a hill and my car just lost all of its power and a weird noise was coming from the muffler and it started sputtering like stalling then it shut off.It wouldnt start but all the lights and everything worked.i had to push my car home.So i dont know what the problem is.can anyone help

when i say cold i dont mean cold as in tempeture well i think its either the main relay or the coil.Anyone?