Another issue might be you have not enabled your browser settings. This means that you should delete all your cookies as well as your browsing history; this is done differently depending on your browser. Another reason could be you might not have Flash installed. Flash technology is one of the most important software available currently that enables people to play games through their software or even view websites which are flash enabled. For this you will need to go straight to the Adobe website and check for the latest update of Flash and download it onto your computer.
You can also try logging in on another computer if you have one to hand or just try a friend's laptop to see if the same problem occurs.
If you do not have this then you might need to go directly to the Flash website in order to download the latest updates to enable you to play and go onto Farmville. You might need to get in contact with Zygna who are responsible for making the game and managing it online. If you are still struggling and experiencing technical issues with Farmville then it is advisable to delete and remove the version you have already and find the application again.
Then all you need to do is go and install Farmville again and switch off and restart your laptop or computer accordingly. You may even need to create a brand new Facebook in order for Farmville to work. But do be warned this is only as a last resort.