Welcome to Tom's Hardware, spartanpradeep!
First, I'd advise you to check Disk Management and Device Manager in your PC as well as your laptop and check if the HDD is recognized there. You might want to try to
change the drive letter in Disk Management and
uninstall & reinstall the hard drive as a device from Device Manager. While there, you can also make sure that you have the latest USB hub controller drivers for your PC and laptop from their manufacturers' websites.
I'd suggest you try plugging the HDD internally via SATA and see if that will make it visible and accessible from your PC.
Keep me posted with the troubleshooting!
Good luck!
SuperSoph_WD