Early 2015 MacBook Pro battery not charging
The lack of a charging indicator light is not a good sign, as it implies a hardware problem of some sort (i.e. cable, charger and/or MBP).

However, one thing you could do is reset the System Management Controller (SMC) to see if that resolves the issue.


Shut down your Mac
Unplug the power cable from your Mac
For 10 seconds, press and hold at the same time the shiftcontroloption keys (on the left side of the built-in keyboard) and the power button
After 10 seconds let go of all keys and the power button 
Plug in the power cable
Turn your Mac back on with the power button.


If the problem still persists after doing this, an easy test to do is to see what happens if you use another charger/cable. If the problem still persists with another charger/cable, then you really should run Apple Diagnostics (you can also run diagnostics in the meantime if you haven't got access to another charger/cable).

Run Apple Diagnostics

Follow the steps below to run Apple Diagnostics:


Fully shut down your Mac
Restart your Mac
Immediately press the D key and keep it down until you see the Diagnostics screen appear
Wait for Diagnostics to finish (this typically only takes a few minutes)
Once complete, one of two things will appear on the screen:


a No issues found message
a brief description of any errors found plus further instructions

If the diagnostics test does find errors, take a note of what they are


Note: If pressing and holding the D key at Step 3 doesn't work, start again at Step 1 and, at Step 3 press and hold both the OptionD keys instead. This will try and run diagnostics from the internet instead, so you will need to allow more time for it to complete. 

Regardless, take a note of what happens and let me know how you went.