I would try the following steps (in this order, until one succeeds or all have failed):
1) Completely turn off the external drive and the PC and turn them on again. If the drive does not have a real power switch, unplug its power supply and plug it in again.
2) Unplug the USB cable at the PC side and plug it in into another USB port.
3) Use another USB cable.
4) Replace the power supply of the external drive (perhaps a friend can borrow you an appropriate one); if this is not possible, at least measure the output voltage and compare to specification.
5) Connect the external drive to another PC.
6) Dismount the housing of the external drive and connect its HDD directly to the PC.
If all steps fail, including the last one, probably the HDD in the external drive is defective. If all steps but the last one fail, the housing of the HDD or the electronics which translate from USB to SATA (or whatever the HDD's connector is) might be defective.