Android - Cannot connect to external IP address over mobile 3G/4G network using sockets

Question

Right now, I am writing a server/client program to allow a user to control different parts of their computer from an android phone on the fly. The server runs on the computer and the client runs from the android phone. I am using socket programming to do this, WinSocket on the computer and Android/Java sockets on the phone.

What Works:

1. The server on the computer end works.
2. When on the same wifi network, the client on the phone can send and receive commands to/from the server.
3. The server is accessible from outside the local wireless network it is connected to. I tested this by using this open port checking tool to send a request to the server. The server can successfully receive the request, and the port checking website reports that the port I am using is properly forwarded.
4. When using an app on my android phone that tests open ports, my server gets the connection request over 3G/4G.

Now for my problem. When I try to connect to the server running on the computer from the client on the phone, when the phone is connected to the internet through 3G or 4G, the socket does nothing and throws a socket timeout exception, and the server does not receive any connection request from the phone. I don't understand this because, like the 4th thing above, the port checking app I used can get through to my server program, but the code I'll post below doesn't do anything when running on 3G/4G.

String hostName = "SERVER_NETWORK_EXTERNAL_IP_HERE";
int port = 58587;
SocketAddress address = new java.net.InetSocketAddress(hostName, port);
sock = new Socket();
sock.connect(address, 5000);

The network activity indicator in the status bar at the top of the screen does not report outbound network activity when running this code, however if I am connected to wifi, everything works correctly. Anyone got any ideas?