I assume it is a USB connection? Does it also have a power adaptor or a USB dongle that has 2 USB connectors? If you cannot get it to power up, the only other option to retrieve your data is to take the HD out of the case and connect it to a PC or laptop using a SSD or SATA to USB adapter and see if you can get the PC to recognize it.
Answers & Comments
Sounds like the power adaptor has failed. (Possibly a broken wire at the connector).
I assume it is a USB connection? Does it also have a power adaptor or a USB dongle that has 2 USB connectors? If you cannot get it to power up, the only other option to retrieve your data is to take the HD out of the case and connect it to a PC or laptop using a SSD or SATA to USB adapter and see if you can get the PC to recognize it.