Check for Water Damage
The Game Boy Advance SP is a very rugged and durable game system, but like all electronics is prone to water damage. On the bottom of the handset there is a bar code and serial number, colored in black and white. If there are pink water stains on the bottom, it is likely the system has been exposed to water and needs to be returned to the manufacturer.
Check the Battery
Most problems with the Game Boy Advance SP can be linked to low charges on the battery. Plug in the SP and allow it to charge for at least 1 hour in the off position. After charging, unplug the SP and then turn it on without a cartridge in. If the Nintendo screen loads, play games as normal. If not, it's likely the hardware is damaged and must be replaced.
Check the Cartridge
The Game Boy Advance SP handset is very durable. If a game is not loading correctly, or freezes up, remove the cartridge while the handset is in the off position. Use a dry cotton swab to wipe out the exposed circuits in the cartridge as well as the handset slot. Turn the handset on as if checking the battery above. If the screen loads, then insert the game and reset the handset to test the cartridge.