Check to see if there is a power button on the enclosure.
Try using a different USB port.
Try using a different USB cable (I have had many an issue with drives not working due to the cable, as the ones that come with the enclosures are generally shotty at best).
If neither of those help, check in device manager or disk management to see if there is a drive listed that doesn't have drivers or isn't initialized.
(If you're not sure how to get there tell us what OS you're using and we can give you specific directions to these, though generally speaking you should be able to right click on Computer, and click Manage to get to them. You will see them listed in the left pane.)
It could be that the drive simply does not work anymore, especially if its been sitting idle for many years.
As JHM mentioned, you could check the BIOS as well to see if its recognized there.