most ext hard drives inside have a small power supply and controller board and data cables. if you are lucky you may have broken the controller board or pop a cable. your better off poping the drive out of the case and se if it spins up. if it a sata drive just temp connected to your pc. if the hard drive when in your hands is not spinging or spins up and down. dont try and do a data recovery on the drive with software. you damaged the drive itself and your best bet is to have the drive rebuilt.
Unfortunately, most external storage drives are purposefully designed so that the hard drive cannot be removed and simply plugged into a desktop.
I would start by downloading diagnostic tools from the manufacturer. Western Digital, for instance, has tools that can troubleshoot the drive. If the drive isn't recognized by windows OR the diagnostic utility, then your only option is to take the drive apart and attempt to remove the hard drive. You can then plug the hard drive into a desktop PC using SATA cables and access your files through windows or perhaps diagnose the drive with those utilities.