1st option - Hope that it's this one
This all just says it's a read error. Most likely the pins on the gba cartridge are dirty or oxidized. A read error can do anything from freeze the game to making information unavailable (like save files). So it explains all of your symptoms.
The freezing on boot is the diagnostic giveaway here. Remember the old NES games? (I might be dating myself here) You would sometimes have to blow dust out of the cartridge to get it working. While blowing on it was actually a stupid thing to do (your adding spit that is worse then any amount of dust) the idea was correct. GBA is much more advanced but still has a lot of pins made out of not as reliable metal as the DS cartridges.
Here is a basic tutorial on how to clean it. Not the best but it will probably get the job done. Pay attention to the part of not over-saturating the q-tip. And make sure the cartridge is completely dry before trying it again. This means waiting an hour or more after applying water. If you have ethyl alcohol instead of water it will clear in a couple minutes: http://www.wikihow.com/Clean-a-Gameboy-Cartridge
If this doesn't work switch water out for deoxidizer. Deoxidizer is intense and can cause a lot of damage if not used correctly so pay close attention to the directions. http://www.amazon.com/Purple-Metal-Polish-deoxidizer-Combo/dp/B005WWMP86
Of course you may have to do this process to the DS-Lite as well.
2nd option - your game is sol
GBA games had a lot of wiring in them. They used actual circuit boards to store and access data. The DS games are simply funny shaped flash cards. With the more rudimentary boards it was easy for breaks in traces (wires etched onto a circuit board) or even failures inside of one of the chips. If this happened it is not possible to repair. Repairing a trace with solder doesn't work as the trace is coated on top and the solder will not actually make contact. And the boards are usually multiple layers that you can't even see. You'll just have to find an flea market or classic video game shop and buy a new copy.