What are the names of all the parts of a computer laptop?

The major component parts of a laptop are as follows:
LCD screen.
Hard Drive.
Optical Drive (BluRay/DVD/CD) though not included with a the now common netbook, a relatively new classification of portable computers.
RAM chip(s).
DC power Board.
Wireless/3G internet card.
Speakers.
Keyboard.
Trackpad/Touchpad.
Battery.
Logic Board.

In modern laptops you will also find a built-in webcam as well as a built in microphone, both usually located within the bezel of the LCD screen.

The logic board houses a (usually) non-removable, non-upgradable CPU and separate GPU chip; these are the Central Processing Unit and Graphics Processing Unit, respectively. There are also connectors for the items listed above and at least one heat sink and fan that helps to vent and pull heat away from the CPU and GPU.

It is here on the logic board that the headphone and microphone jacks, as well as a video-out ports and your USB ports can be found. Often soldered onto the board and often difficult to replace should one of these items become damaged or fail. There is also a small button-style' battery that helps preserve the computer settings and the time should it be not connected to a power source. The rest of the logic board is comprised of hundreds and hundreds of different parts, most of those being transistors, resistors and data cables and electrical pathways.

Some manufacturer's use an internal frame to help offer some stability and reduce the laptop from flexing but most do not.

All that remains now is the case; the backside of the LCD is often called the 'lid', the keyboard housing and track pad, along with the palmrest, are often referred as the 'top case' and the bottom of the laptop is most often referred as the 'bottom case'. Most laptop cases are made of plastic while higher-end laptops (such as Apple's MacBook Pro) are made of metal, aluminum in this case.