Seagate external drives usually have a poor power supply (and controls), but fortunately there may be hope for the drive that's inside.
You should be able to open up the external housing, and take the drive out and connect it to the internal wiring of a PC.
The PC should have plenty of power and has its own controls. This may be able to get it back from the dead. This has worked for me a couple of times already.
It does require some computer knowledge though.