The trapezoidal connector is proprietary to your laptop. If you take apart the drive sled or housing you will see that the connector has another end which connects to the actual drive. The drive's connector is a 44 pin IDE cable.
To connect the drive to the WebPlayer, you need a 44 to 44 IDE connector. You coudl also use a standard IDE drive, which has a 40 pin connector, with an adapter. But, a standard drive is kind of big to fit in the WebPlayer case, so a 2.5" laptop drive is better.
You can get laptop drives on eBay cheap. I paid 42 bucks for a 2.1 gig Seagate new with a warranty. You can get 6 gig drives brand new for under $150.