Default Moto G sometimes won't recharge from pc usb port

My gf bought a moto g and it's working good in general, but weirdly, it has some problems charging off some usb ports or other chargers. I have a generic charger for my htc one for example, which the moto g won't charge off of. I also have a generic USB cable form which I can charge my HTC one or my mom's samsung s2, but with the moto g, something odd happens - it starts charging for a few seconds but then stops charging, just enough time to show the "phone connected as media storage" notification. I tried one time turning the media storage mode off to see if that might be the problem, and it seemed to work, but after a while we saw it stopped charging. The battery also dropped like 40% during the night and that amazing battery should not even drop like 5%, but that seems to be just battery statistics being corrupted or something, not a real problem probably need to let them reset.

Anyone here had a similar experience? Any fixes?