A few more questions for you Lemmi, Where is the battery located, under the hood or in the trunk? Has the car been repainted, and were the engines repainted when rebuilt? How old is your battery? When the engine is hot and will not start with the starter, does the starter roll the engine over at a normal speed and the car will not start, or the engine barely turns over?
Have you added or does the car have any aftermarket electrical accessories like a big stereo, driving lights, computer hookups/outlets? Have you checked the timing?
My first thought is a weak battery or poor ground because it will start with a jump when hot... Cal