Welcome, @sanjeet sodhi!
I'd suggest you try using a different USB cable with the external HDD as well. It's possible that the cable is faulty and that's why you are unable to get the HDD powered up and located anywhere. If the problem still persists on all computers, it's probably best to contact the reseller's/manufacturer's customer support. You mentioned that the external hard drive is relatively new, so it should still be covered by the warranty. The customer support should provide you with a replacement product and assistance regarding the RMA procedure.
If you have any important data on the drive, though, you might want to ask them for data recovery company referrals as well.
Best of luck!