What I'm saying is when I plug it into my laptop it lights up, and stays lit up as the drivers are found and installed. Devices shows the brand and look of the controller, and the controller remains lit up through it's LED lights.
On the desktop when I plug it in the light comes on briefly, then it turns off, then windows returns with "Unknown Device". It's as if the usb driver can't identify the controller, nothing is installed, not even the generic windows driver and I get error 43, meaning the device is shut off.
If you plug it into the PC without the drivers, it should switch to charging mode. Pressing the PSN button will then turn on your PS3 or swap it into searching mode.
The PS3 controller is technically off if it isn't synched which is where the driver is required. Like I was saying, you can't connect it and use it until you install a driver, and your laptop makes me think at some point you used a third party HID controller (possibly because laptops used custom keyboards with custom key mapping and thuse use legacy HID controllers anyways.)
Try the suggestion posted by sze5003, from my recollection that is how it works.
Install MIJ. Open MIJ, it has a button that says something like "find PS3 controller" or something of the sort. You have to press that button for it to turn on the PS3 controller. As far as I remember for MIJ, you always have to do this before using the controller, because once you reboot your PC the controller will swap back to charge mode (and if your USB port isn't hot, the battery will slowly drain.)
EDIT:
Woof just about everything "gaming" related is blocked, but Balla this is the screen Sze refers too:
There you hit load drivers, it takes a few minutes, then you can go this screen:
To set it up. Note sure how old these screens are but they are how I remember them when I last used it, and that was to play Batman: AC last year.