No, you do not need to buy Origin Access to play online. That is a service for something else completely and you can see the details here if you are interested: https://help.ea.com/en/article/origin-access-details/ .
As for your problem, this usually means you maybe having connection problems with Origin. Make sure you are first connected to the internet and check if you have any problems with your connection. If origin still wont go online, please log out and exit origin and then launch it in administrator mode and see if that works.
You could also try to access battlelog from here: http://battlelog.battlefield.com/bf4/ , log in manually and select a server and start playing etc but make sure you at least have Origin running.
