Apple hardware issue. Battery not charging, service recommended
The response codes from Apple Diagnostics are listed in https://support.apple.com/en-us/HT203747:

PPP003: There may be an issue with the power adapter. Disconnect the MagSafe power adapter from the computer and the power outlet, then reconnect. Run the test again.
If this code appears a second time, further troubleshooting may be required. Contact Apple or take your computer to an Apple Authorized Service Provider or Apple Retail Store to determine which service and support options are available.

PPT006: The battery requires service. The battery is not functioning normally, though you may not notice a change in its behavior or the amount of charge it holds. You can continue to use your battery before it’s checked without harming your computer.
Contact Apple or take your computer to an Apple Authorized Service Provider or Apple Retail Store to determine which service and support options are available.


So there still seems to be a problem either with the power adapter or the battery. Without access to the hardware it's impossible to analyze this further so it's probably best to visit the Apple Store again.