That's a hardware problem, either with the power adapter, the battery or the motherboard. Since it's only 6 months old they should fix this under warranty. So back to the shop.
I have a Medion Laptop P7648. It has just been six months. It was working perfectly fine until I discovered that it was not starting with only the power light on. The next time I saw that nothing was functional. The power button didn't show any light, neither was the charging light on when connected to the adapter. Please help me.