Find the correct department that can utilize your skillset and when messaging them, try not to sound desperate and also I forget to mention this before but have some kind of side-project that you do that shows off your skillset. For example, I post small animation videos on FB almost every day ( except when I am extremely busy like now.). It can serve as a type of portfolio which will benefit you. Most importantly, don't take the rejection too personally and don't get discouraged - take it as a learning process.