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Yes, all the cables that are removable can be reused.
It could be the charger port is defective, even though it is new.
Have you tried another charger cable and plug? It will charge quicker over mains power than over USB charging.
If the computer doesn’t recognize it either, then I would guess that the new part is probably defective, if it was recognized with the old part before.
I would not recommend putting your phone in the microwave......it could cause serious damage to your phone and the microwave. There are metal components and the battery, which you do not want exploding in your oven. Use a heatgun or hair dryer to warm the battery cover, but you don't want to get it too hot either.
The 2016 Model is different, so I would look for the model specific repair information:
Samsung A3 2016 Model - A310F Display / LCD Replacement
This is a guide I wrote for the 2016 model...Hope it helps!
Normally you can find it online at any electronics parts supplier......or eBay. the part itself isn't too expensive but will depend which country you live in.