Possible internal damage, especially the HDD mechanism internally. What's the brand/model of that external HDD? As for data recovery, try inquiring these professional data recovery services...

- MDR Data Recovery Solution
- Adroit Data Recovery Centre
- Seamax Data Recovery
- Ontrack Data Recovery, Singapore
- Data Recovery Center

Note: These professional data recovery services are rather expensive, expect the pricing to be in the hundreds if not thousands... 

Just a discussion, a "fall down" or "dropped" HDD, shouldn't be the data on the disk itself is still intact? or electromagnetism on the disk itself (that storing the data) will be loss on the disk due to the fall?

As I reckon, when the HDD is not in operation (when carried along), a dropped could means damage the mechanical part of the HDD, as head is parked during idle (non-operation), there shouldn't be any scratches on the disk.

Assuming that was true, the data recovery centres are doing a poor job of communicating that potentially crucial information to would-be clients. Then again, it might be to milk the most out of their clientele by not differentiating an easy job from what may be a very difficulty job.

JiesonJason, was your external HDD powered when it fell?