I successfully used OEM cables and chargers. Note that most OEM chargers won't do fast charge because their throughput is too low. In fact, some have a throughput that's so low, the phone can use more charge than the charger provides - which could explain the symptoms you're seeing. To check if this is the case, try turning the phone off and leaving it to charge overnight.
If that's not the issue, then it seems to me that there is a problem with your OEM charger, the USB cable or the phone itself. Probably not more than 1 of these
You need to try to isolate which is the problem. To do this you could try:
- using a different cable with the OEM charger
- using the same cable with a different charger / USB port on a PC
- using a different cable with a different charger / USB port on a PC
If the problem is either with the charger or the cable, these should help you identify which it is.
If none of the above combinations work, then I'm afraid the problem is with the USB port on the phone and it's time to call Google for a warranty repair (I've done this in the past and it's not too painful a process - just make sure you have everything backed up).