ATMega328p won't communicate on ICSP
When I first saw the question I was about to suggest reflowing the chip.

Why don't you try to upload the bootloader program on the arduino and flash your chip with the arduino instead of using the chinese ASP? 

Here's a tutorial https://www.youtube.com/watch?v=xl-XQ_te8zM

I hope this helps. I could suggest that if this does not work, replace the SOC. Maybe you burned the 328P