Thanks for the reply @jeremy.
Let me elaborate a little more. I will also quote the exact error message.
1) Yes I have G+ account.
2) WordPress is listed on G+ as authorised application.
3) I tries to connect Jetpack using various browsers on Windows 7 and Linux (Ubuntu).
The error message I get is:
You've reached this page because we have detected that Javascript is disabled in your browser. The page you attempted to load cannot display properly if scripts are disabled.
Please enable scripts and retry the operation or go back in your browser.
Java scripts are enabled. I am not a programmer. However I am very well aware of computers and know for sure that Javascripts are indeed enabled on all the browsers I tries on both the operating systems.
The problem has been persistant since G+ connect feature was released and over two (maybe more) updates of WordPress.
Thank you for your prompt response. I will also keep looking in this matter to see what stops me from connecting to G+.