The closest matching common mode choke that I found is made by Pulse Electronics with part number PE-1210CCMC601STS. The footprint, impedance @ frequency, and max current rating are exact to EM10, but where it differs is that its max DC resistance is 120 mOhm. Whether or not being short of 80 mOhm is acceptable is unknown.
However, both iFixit and Retro Video Game Repair states the power supply filter is a concern when you don't see the LED charging indicator light up. That means you can rule this one out, which leaves the IC charging chip.
The part number for this chip made by Texas Instruments is BQ24072. Here's a quick search from digikey: