I had the same problem. It was because of the battery. Not the charger, not the cable, not the GBA itself.
I solved it by plugging an unplugging the cable several times. I slowly noticed a little increase the time the orange light was on (not reaching a second). Then it stayed on and charged.
My guess is that the battery was in a deep-dichrge state and that refreshed the chargin protection and kickstarted it.