First and simplest thing to try (after trying another USB port which you have already done) is to delete its entry from device manager.
The following is based on the fact that your second computer can see the drive, and this in theory eliminates the possibility that the HDD might be broken. Unplug your HDD first.
Click on your Start menu and then right click
on Computer. Underneath the top option, which is 'Open', you'll have Manage
. You may need to click 'Allow' or 'Yes' if User Account Control pops up a box.
In the Computer Management window you should see three panes, or three columns. The left
pane is the one we want first, and toward the bottom it will say 'Device Manager', and if you click on that the middle
pane will change to show a long list of items. You want to click on Disk Drives
I am hoping that although you cannot see your drive in normal use, that Device Manager will still display it. If it does, then simply right click
on your HDD which is not being detected and select Uninstall
. This will then remove the drivers
for that drive.
When it is complete (it should take just a few seconds), plug the HDD back in and hopefully Windows will be able to find it.
If the drive does not show up in here either, of course let us know.