I had the exact same issues, They've been resolved....
After talking several times and hours with Tech Support and trying all tips and tricks from any and all forums... the problem persisted!
I noticed/inferred that everyone who's having the problem was originally using REL03, so I went out and exchanged my NSZ-GS7 hoping something would be different.
After turning on and running quickly through the initial setup, I saw that the software was REL01.
$$$ I was able to access PLAY STORE immediately!
$$$ Within a minute, a system update notice popped up automatically!
Soon, I had a REL06 and all my favorite apps up and running.
If you can find it, maybe you can try installing REL01. Good Luck.