I've had issues with old AC adapters/power supplies/chargers that even said they provided a little more than 1.0 amp @ 5volts. Now I always use one that is at least 2.0 amps or better @ 5v.

For a battery that's been unused for that long I'd expect issues. Once a rechargeable battery is put in service, I usually have issues when they go unused for and long time. But I haven't let my Di2 battery go unused that long. So I have no idea what it'd do.

I also agree with mpetry912 The Di2 charger (SM-BCR2) Shimano gives is pretty cryptic. Other than charging or not charging, I don't know if Shimano really gives much info on what it's telling you if it even does.