New USB external HDD won't show in "Computer"

New external HDD won't show in "Computer"
l Have searched a lot, but only find comments directing me to Disk management and
Device manager.
The Ext. HD is not showing there either. Power light is on.
This is a Lacie 2 TB Minimus USB 3.0 External Hard Drive
http://www.jr.com/lacie/pe/LAC_301967/
No "Doorbell" sound when I plug in or un plug the USB connector.
The LaC ie troubleshooting page tells me to go to device manager, but like l said, it's not showing there either.

Plus, it seems to have knocked out several of my USB ports,
and I had the warning flag next to several of them in device manager ,but I was able to get them back by right clicking on each line one at a time, Un installing, and right clicking
on the heading for the group, and selected "scan for hardware change" Then in the tray, I saw Driver was installed, or device is ready, something like that.
All the ports seem to be working now, and the yellow flags are gone.
I did then try the External drive again, but it is still not working.

I also installed desktop manager, but it's telling me to plug in my external drive, and then to re start my device.
And if I start Desktop Manager it says,
"No LaCie Desktop compliant device found."

So I have another computer that shares this monitor,so I shut this one down, and hooked up my usb keyboard and mouse to the other older desktop system running XP, and the older computer does recognize this external hard drive. It is in My computer on the older XP system/computer.

So I shut that one down and started this one, and it does not show up on this computer, but then I noticed my keyboard would not work.
Had to switch the keyboard USB ports to the other front USB port.
And I had the yellow flags back in device manager again.
Had to un-install again and let the system re install ( selecting "scan for hardware change)
Windows 7 Home premium, 64 Bit, Compaq Desktop, model 2010
Any Ideas? Hope l have provided enough information.
Thanks,
Tony

For some reason this thing will work in the front 2 ports, and the 2 lower ports on the rear, but not the upper ports on the rear.
I don't know why???????
Yet my Mouse and camera will work on the upper ports.
So it is now showing.

Some ports, if your system has USB 3.0, are dedicated and need the drivers. In Device Manager do you show any USB devices with a 3.0 annotation? Do you know if your system has USB 3.0 ports and which ones they are?

NO, this system is USB 2 only, it is a Compaq model 2010.