DS won't turn on after charging?

I recently grabbed my old original DS from home and was happy to see that it still powered on without being charged after several years. Later on, I plugged it into a wall outlet using a GBA charger and watched the orange light illuminate for about a second, and then turn off. Now it won't power on, and the orange light won't stay on even if held in different orientations. I opened it up and saw some black corrosion (I think?) around the bottom of the charging port. Should I attempt to replace the battery or clean the port? Is it fixable without replacing the port completely?