Based on what you wrote, it sounds to me like a very real possibility that the impact caused physical damage to the data storage platters inside the drive itself.
If the data is unreadable, but the electronics are okay, then the drive will show up as a physical drive but it's anyone's guess how the operating system will list the partitions on the drive. In your case, it seems to be unable to read the partition table, and thus does not list any partitions. In such a case, the drive will also show up in Disk Manager or similar tools but with no partitions, and possibly listed as damaged or unreadable.
Normally, the first step here would be to POWER OFF THE DRIVE. If it has suffered internal physical damage, which is always a possibility after it has been exposed to physical shock, keeping it powered up and spinning will definitely not help, and depending on the specific type of damage can very easily make the damage even worse. Wikipedia has a whole article on hard disk drive failure which, while it has some issues, isn't outright bad; if you are curious about the various ways hard disk drives can fail, it's a good place to begin reading.
Given that you have already kept the drive spinning for some time after the damage was incurred, you certainly can keep trying with software-based solutions such as Recuva which Tetsujin suggested in a comment. (There are other tools as well.) A perusal of the hard-drive-recovery and partition-recovery tags will likely bring up several other suggestions for tools as well. Copy whatever such tools are able to find to some other drive; consider your current external drive to be broken and to be removed from service.
If you have no backups and the data is important, forget about trying to fix this yourself. Just power off the drive, and contact a reputable data recovery company; there are several out there, and prices have gone down over the years. Two signs to look for is willingness to work under a non-disclosure agreement (data recovery companies often handle sensitive data, and even if your data isn't sensitive, NDAs are par for the course in many cases), and either a fixed price offer or being able to send your drive in (for free or at a fairly nominal cost) for evaluation and getting a price quote before any additional work is done. Note that a new drive is usually extra, but you'll want one anyway. A reputable company will not offer to restore a drive broken from physical impact and send it back, since the state of the physical storage media is at best unknown; they will be copying the data onto new media, most likely a new hard disk drive.
File recovery from damaged media is almost never a best approach. If you have backups of your files, I recommend buying a new drive and restoring your most recent backup onto it. It will be quicker, easier and more likely to yield good results at the lowest cost.