CAR WONT START

Hello, I hope someone can help me, I have suddenly been having problems with starting my car up. I took it to the garage, they replaced the battery, it was ok for a day then wouldn't start again, took it back to the garage and they gave me a new starter relay and then it worked for a day then back to square one! It is so far cost me 100.00 to fix that, the battery was knackered anyway so needed to be change. It is fine when we jump start it and then if I've been driving it for about 20 - 30 mins it will start up straight away when I turn the ignition off just when it is left overnight or off for 3 or 5 hours. Do you think it could be the starter motor? I don't know anything about cars and this is stressing me out!!!