The original eSATA specification does not provide power. You'll need a USB cable or wall adapter to power the hard drive. The new eSATAp specification utilizes the USB bus to provide power over one cable, but is relatively rare.
The easiest way to be sure if you have an eSATAp device or not is to check the plug. This helpful image from Wikipedia shows the difference:
The laptop model you listed uses an unpowered eSATA interface and the hard drive you listed is an internal hard drive that uses the original SATA interface, so you will need a cable that accommodates that rather than any plain eSATA cable. While most 3.5" internal hard drives require more power than USB will provide, Western Digital's Caviar Green series reduced power requirements should be met.
They make cables that convert the standard SATA data/power connections to eSATA for data and USB for power (like this example image). However, a far better option IMHO is to buy an external drive enclosure, which is essentially a box you insert your hard drive into with cables provided for USB power and eSATA data. The enclosure will protect your bare drive from damage, and as far as I can tell, aren't that much more expensive than regular cables. If you decide to go that route, make sure the model you buy accepts 3.5 inch SATA hard drives and allows for USB power and eSATA data output. Some models additionally offer USB data connections and/or AC outlet power connections as well.
And here is a eSATAp to SATA+SATA Power so that any standard SATA drive can utilize the power from the eSATAp connection without the need of a USB connection, and only requires the eSATAp connection on the computer end: