I would try removing your google account (Settings - Accounts - Google - tap the 3 boxes in the top right and Remove account.
Then add it back and see if that helps.
So, if you cannot sign into your google account, are you sure you know the password to it?
yeah i never lost pass
If you did a factory reset to put it back to the out of the box condition, and it will not accept your google account password and you are sure it is correct, then I am out of ideas.
i think this problem after instal DNS changer at market but maybe .. my dns already set normal again but not work
If you did a wipe, the DNS settings should have been reset to defaults.
I have never messed with a DNS changer app myself though.
after I browse on the internet about this problem turns out there are several different android devices are also experiencing the same thing .. so its bugs Android OS?
I have seen where there are some sync issues with some Android OS versions, but it will still let you add your account to the tablet in the Settings - Accounts area.
This is a firewall issue. I just found this out because I was having the same trouble with the grey wifi icon (hence, why I'm here, lol). The software firewall on my dsl modem was set too high, so I set the firewall to low and sure enough, my wifi icon went blue again. The same will happen with your cellular icon on your phone, if you don't have any sort of data package on it - reference to AT&T GoPhone, here, on a Nexus S. I didn't have data on my phone for the longest time, like nearly a year, just talk and text (but I could send and receive picture messages, which means it was hitting AT&T's data servers fine, just not Google's), and then recently got data on it, and it went that pretty blue we all love. So I say, check any firewall you may have in place or as mentioned, the dns changer, because yes, it will happen with that too.