How come I can't connect to Amazon RDS after setting it up?

It is "just hanging" as you have not configured the firewall to accept mySQL connections from your other instance, as such the packet is being dropped at the firewall level, to resolve this you need to:

1. head into your AWS console
2. EC2 tab
3. Note down the security group of your mySQL server (well call this SG-MYSQL for now)
4. click security groups on the left of the console
5. click your group in the center menu SG-MYSQL
6. click inbound tab
7. select mySQL from the list, add the details of your client server and save the rule

NOTE the source IP for the server will not be your elastic IP (in most cases anyway) you will have an internal ip on the device (ifconfig on linux will show you this).

By default RDS does not allow any connection that is not specified within the Security Group (SG). You can allow based on CIDR addressing or by Amazon account number which would allow any EC2 under that account to access it.

Fixed.

Had to grant access to it in the security groups under the DB...