Hey Daniel,
Make sure the charger you are using is the proper voltage to charge the device. If it's too little, it will not take a charge, you may see a little light like you said.
The charge cable may not be the problem, it may be the port you are plugging the cable in to. This port is soldered on to the motherboard of the Gameboy, and if it has become loose, you will not be able to charge it with ANY charger. If you have basic soldering skills, this is not a difficult repair, if you do not have an electronic repair background, I would advise selling it for parts, and purchasing another one.
Have a good one, sir. :)