Sorry to hear of your current issues. It may be worth taking a look if your RDS security group has been properly configured - you will need to refer back to the AWS troubleshooting documentation. Another suggestion is to download a database tool such as DBVisualizer or SQuirreL, and attempt to connect to your database on AWS with these programs instead of YF, which should demonstrate whether the issue is a Yellowfin issue or not.
If these suggestions do not assist, could you advise what version / build of Yellowfin you are using to try and connect to the AWS data source?
Hope to hear from you soon,