First that iPhone you have? Update (09/11/2015): Sorry I know your iphone now nothing without PWR and Home button, but now you must full restore on IOS 6.1.6 than first with redsn0w hactivate, than always using redsnow first make upgrade iPad BB than downgrda BB and again using redsn0w make JB than yuo need to install Ultrasn0w from Cydia to unlock, in all steps yuo need to pres home and power buton in same time, it is problem now but your phone was poorly JB. after JB need install from Cydia Resset All kiler in order to prevent resset all because so you kill phone.
First you must try call with earphone or BT handset and if no change, the problem is probably the motherboard (audio chip) , have any tone? rings, music in the audio or video recording?? This will be very important answers.
No without passcode and you must have problem if frst time conect to iTunes need confirm to trust this computer, but if frend have Apple ID all app instaled from Appstore have only enter Apple ID and pass on new with coonect on net and install from AppStore, data annd settings are lost if not previously mada back-up to iCloud?,,,try sighn in iCloud and if have backup no problem, new sync not possible without new screen and only remains synchronize with the older back-up if there on his computer