I had long noticed that when connecting to W-Fi the indicator in the status bar (the quarter circle shaped thingie) would usually start off as clear then go white, then blue with the number of segments indicating the signal strength.
I'd worked out that "clear" meant that there was no connection (probably could see an AP but DHCP hadn't assigned a network address) but what was the difference between white and blue - sometimes on white you could actually connect to a website and perform other activity so it didn't mean you had no internet connection.
Further observation leads me to this conclusion -
The indicator initially turns white when the local AP assigns a network address to the tablet.
It turns blue once the tablet has established contact with some external IP address (probably a Google one)
This revelation came about when I lost my router's internet connection - the indicator was permanently white and I could connect to other devices on my local LAN (these use NETBios for named address resolution rather than DNS), but not to external sites.
So it looks like there is some test that the tablet does that proves an Internet connection rather than just one to the local AP before turning the indicator blue. You may have internet connectivity on white but it hasn't been proved. The lack of connectivity may be local to you or may be in the ISPs network - in my case I believe the problem was probably between DSLAM and the core network.
I know someone asked about this recently but I cant find the post to reply to it
BobC