What place can recover hard drive data from a dead iPhone 4?

My phones battery circuitry short circuited from water damage. So my iPhone can't charge and is completely out of battery. Is there any place that can take out the hard drive and recover the data (music, contacts, pictures) and put it on my current phone?

Your iPhone doesn't have a "hard drive" that can be removed from it. It has NAND flash memory that is attached directly to the mainboard PCB for storage. Your only real option is likely a data recovery service. I would recommend this one. I've never used them for a phone, but they are great for external hard drives and flash memory in general.

http://www.drivesaversdatarecovery.com/devices-supported/apple-iphone-data-recovery/