As Philip brings up, "removing drive from enclosure" is about your next step. I don't know this model of enclosure but, in the last 8 years or so, Seagate's used a plastic clamshell design (top piece, bottom piece) that are clipped together with real, genuine plastic. So I have to snap those off (crack!) by inserting a flat-head screwdriver into a side-seam, and twisting it. Probably at the corners, first.
Some had 4 clips, some 6.
But first, I'd look for screw-holes deep on the underside or back of the case. Any dark dank hole is probably a bolt-hole, probably philips-head type.
Once you get the case open, there will be a few screws to undo and the hard drive can be extracted.
At this point, I'd open up my computer and plug in the power-connector to it, and hold the hard-drive in my hand to see if I could detect 'motion', vibrations - anything to indicate life!
If so, then you can buy a new external case (well, an old IDE version) and insert the drive there, or you might get a USB-to-IDE/SATA converter kit and attach the drive as a bare external.