Please check the file system of the External Hard Disk. For ex, FAT 16 or FAT 32 or NTFS or ExFAT . And please check your OS. Some of the file systems are not recognised by Linux OS based PCs depending upon the version of the Linux OS and so on. Basically, if your TV detects your External Hard disk, there is nothing that should stop it from getting connected to your PC/Laptop. It is quite evident that your Hard disk is not faulty as you have mentioned that you can access it over your TV
One thing to do is to update the drivers of the USB3.0 and USB 3.1 Ports on the motherboard of your PC/Laptop. That is one issue which can stop it from getting detected on your PC/Laptop.