SCR is for sure not faulty...
I have changed my mind, I am not as sure as I was...
I had a look at KP20A datasheet and it's a low end, low cost chinees brand SCR.
My experience has always be with quality brand SCR's (GE, Westinghouse, Semikron, Teccor, Ixys, AEG/Eupec, Philips, ...) and they are very reliable semiconductors.
They can be protected by ultra-fast fuses.
When they are faulty, they generally have anode/cathode short-circuited by heavy overload (fused junction by overheating).
I remember some manufacturing problems with SKT40 (too weak case) and also very rare cases of loss of sensitivity of gate of very old thyristors.
But...but....but...
This KP20A is not a known brand...
Nothing to do with my experience !
It can be a crap quality.
Then, first short-circuits anode and cathode and see if you have a charge current.
I think it would.
Than, remove the short-circuit and measure in dc 20V range the voltage gate/cathode when the charger is working with battery.
You should measure some positive gate voltage around 2 or more volts.
If not, desconnect the gate and measure the gate/cathode resistance. You should read something between 20 and 100 ohms.
If this value is a short-circuit or open, the SCR is faulty/dead.
If the value is correct, the gate drive circuit is faulty.
If there is a positive voltage on the gate, than the SCR is faulty.