First of all check if cable is all OK.
You can start with changing the USB cable. Beside that you can connect your drive to another computer to verify that your computer USB port is working good or not.
In case I guess you have various options to recover data from dead Seagate external hard drive:
First of all check if you have kept the backup of your important data somewhere else like on computer. If you have backup, then you can easily restore your dead hard drive data from the backup.
If data stored within the drive is important and you don’t have backup, then you can use suitable hard drive data recovery tool to recover data from dead Seagate external hard drive.