how can i open my iphone because when i try to restore it from my back up all the files it didn't open anymore & always my iphone have a problem that it automatically shut down then the itunes logo appear then i need it to connect to itunes then restore t

how can i open my iphone because when i try to restore it from my back up all the files it didn't open anymore & always my iphone have a problem that it automatically shut down then the itunes logo appear then i need it to connect to itunes then restore to enable to open it..what should i do?i cannot bring it to the smart center because i lost my receipt..is there any chance to recover it?thank you so much..i already update my operating system to ios 6.1.3 but when i recover my back up the operating system was ios 6.1.2..