|The drive was dropped... Presumably it is not an SSD drive...; rather the mechanical style...?|
I think I would concentrate in transferring whatever you can to DVD and/or another hard drive.. Chances are this one is damaged?
Dropping it likely upset the alignment of the spindle on which the platters etc. rotate...?
You could try the freezer routine; as this "may" allow a better access - at least long enough to copy the contents as above...
Remove the drive from its housing; wrap in paper towel; place in a plastic bag (the type often used for sandwiches will be fine. Seal the bag. Place it the freezer for about an hour half an hour or so. Remove from freezer; unseal bag and let it breathe a few minutes. Then remove drive from bag, loosen (do not remove) paper towel around the drive. Let it breathe about 5-10mins. Then (if possible with a usb-SATA cable adapter) see if you can access the contents any better...? The cable adapter allows an easier test, as you don't have to rehouse the drive to check the drive again...
You may this routine helps - for a short while; then perhaps repeat the freezer routine again.. Likely it may at some stage fail as the drive itself finally "jams up" consequence of possible misalignment of its spindle?
Regardless of success (or otherwise) in copying contents from this drive... regard it as damaged and replace it. Don't rely on it for anything serious...
USB-SATA cables are available on Amazon, Egghead likely too. I have a couple form Amazon and they work fine.
This is one I have - via AMazon.co.uk; and it's also on Amazon.com:
StarTech.com USB 3.0 to 2.5" SATA III Hard Drive Adapter Cable w/ UASP - SATA to USB 3.0 Converter for SSD/HDD - Hard Drive Adapter Cable