This is a Game Boy Advance SP in a Lego Arcade Machine. You will need a GBA SP and a good amount of Lego bricks.
Step 1: Building
You can watch the embedded video or download the Lego Digital Designer (LDD) file below. In the LDD file, i added a better joystick which is not in the video.
Step 2: Picking a Game Boy Advance
There are two types of GBA SP's.
1. The frontlit (AGS-001)
2. The backlit (AGS-101)
The AGS-101 is the better of the two, but both would work fine. If you want to know what your GBA SP is, you can look on the back and it will tell you if its a 001 or a 101.