I check PB check-box and I do see the server list but the problem is whenever I try to connect to the certain server it goes for a sec Connecting to IP xxx.xxx.xx.xxx and then right away says KICKED.

Does anyone have any clue how to fix this and play online?

Also, do you know some servers where people are playing this game constantly - cuz not too many people are on the regular ubi servers.

Thanks guys!

Make sure you do not have -devmode enabled. If you used cheats for the single player game the server will not let you online.

Kicks can also be for high ping, for having extended ASCII characters in your name, for not having high enough graphics settings for water and special effects. Punkbuster can also be configured to kick for known cheats or altered FCData folder contents, even for having certain strings of letters in keybinds that might be used for an advantage.
Punkbuster will also kick you if it cannot verify connection to its master server, something that is not in your control.
If you get an error message, knowing what it is might help determine the cause.