[AC Question]

I lost the original charger on my Note 3 and my battery is completely drained. I've tried a bunch of other micro-usb chargers I have but the phone doesn't show any signs of charging. Even kept it plugged in for a few hours. The chargers work fine on an S3 and Note 2. I thought the phone was dead so I took it to a Bell store and they tried charging it with an original charger and it instantly showed the charging icon on the phone. They wanted $50 for it though, so I declined. Why don't these other chargers work? Some have outputs of 1 amp and others 1.2 amps.

[OceanView]

it should work but maybe the battery was drained beyond the minimal charge point.
You can buy high amp chargers on ebay for a few dollars.

[Rukbat]

You need a charger with an Output line showing at lest 1.2 Amps or 1200 mA. (That's the normal charging current for a travel charger.) A 1 Amp charger probably won't be able to keep up with the phone's battery drain. (I had that problem in my car until I looked at the adapter [with strong reading glasses - where do they get this 0.25 point type?] and saw that it was 1 Amp output. Now, with a 2 Amp adapter, the phone stays charged. (The charger can be any output from 1.2 Amps up - a 30 Amp charger won't harm the phone (I use a 30 Amp 5 volt supply to charge phones all the time. Phones draw what they're designed to draw, as long as the charger can supply that much current.)

Run Ampere when you're charging, to make sure you're getting 1200mA.