I don't know why did I read "black in time", which makes no sense: But as you wrote "my phone was in a back date" – Check your time settings, please!
If your device time is too far off, certificates will cause trouble, which finally results in exactly that: no secure connection possible, and you cannot access your account. In cases like that it often helps to set the time manually (must not be to the second, if it's a minute off it's still fine). Then try again. You can set time adjustment to "automatic" again later.
Background: Certificates have a "livetime", including a start and an end. If your device is outside this frame, the certificate is either only valid "in the past" or "in the future", but not "now". So your device will reject it. Without a valid certificate, the Google Play app won't be able to establish a secured connection, and thus give you an "unable to access" (or similar) error.
Same applies btw. to other apps using secured connections – including the web browser when accessing sites via
https. The latter you can use to check whether you've tapped into this trap: Start your web browser, try accessing e.g.
https://www.google.com/, and see what happens. If you get a "certificate warning", that's it.