Late 2008 MacBook Battery dead

The battery for the model 5,1 Auminum Unibody is different from the White or Black MacBook batteries.

Here's some on eBay http://www.ebay.com/sch/i.html?_nkw=aluminum+macbook++battery+A1280&_sacat=0&_od kw=aluminum+macbook++battery+A1278&_sop=12&_osacat=0

Or from Apple http://store.apple.com/us/product/MB771LL/A

Replacing the battery in the MacBook (13-inch, Aluminum, Late 2008)

Removing the battery:

1. Shut down the computer. Disconnect any cords connected to the computer.
2. Turn the computer over.
3. Locate the access door latch.
4. Push down to release the latch, this sets it in the open position, and remove the access door that covers the battery.
   
5. With the latch still in its open position, gently pull up on the battery tab to remove the battery.

Note: The latch must be in its released, open position to remove or replace the battery and access door.Installing the battery:

1. To replace the battery, make sure the latch is in its open position.
2. Hold the battery at an angle and slide the lipped edge of the battery below the brackets on the outside edge of the battery bay. Gently press the battery down.

To replace the access door:

1. Line the access door up with the bottom case and the tabs in the battery bay.
2. Lower the access door into place.
3. Make sure it is level with the bottom case of your MacBook.
4. Press the latch into place, so it is in the closed position.

See the answer in context

Here's instructions on how to calibrate your battery http://support.apple.com/kb/HT1490

As to how long it should last it depends on the Operating System you're running and how much power intensive applications you run. Lion and Mountain lion are battery hogs.

Also read http://www.apple.com/batteries/