Could you tell me what file format have you chosen when you formatted the hard drive. It arrived formatted in NTFS, right? Please make sure you have selected the correct file format and then connect the drive to the Mac. I would format it in ExFAT especially if you are going to use the drive on both Windows and Mac.
Open Disk Utility and check if the drive is recognized. If it is but with wrong format, format the drive once again and then check if the issue has been resolved. I would strongly recommend you to test the drive on another Mac PC and with another USB cable.
Please let me know if there is progress!
Hope this helps