This tactic may not be possible. Many of the newer USB external hard drives do not contain a hard drive with a standard SATA connector. The manufacturers are short-cutting the hardware to save money, so the SATA connectors are left off the hard drive and off the hardware in the enclosure. Explains why you can now buy an external USB hdd cheaper than a bare SATA hdd of the same size. If I can find the post, with pictures, that I remember seeing on the NCIX product page, I'll post a link.
So perhaps this is only true for WD 2.5" Passport drives, but beware of thinking an external USB drive will automatically contain a conventional SATA drive. It used to be true, but may no longer always hold.
Since you failed to provide specifics, like your other questions/threads, for safety, only general responses can be provided.
Double check cable connections.
Test with another port.
Test with another cable.
Test in another power outlet.
If none of the above suggestions assists,
Look for your external hard drive receipt to identify brand and complete model.
If under warranty,
Contact external drive manufacturer for RMA process.
If warranty expired,
State brand and complete model for any further assistance.
As DanceMan already pointed out,
Depending on model,
Disassembly may not be feasible.
If of no concern, Justintime's response would apply.
Contact a data recovery service company.