I have a Java program that connects to a webserver using SSL/TLS, and sends various HTTP requests over that connection. The server is localhost and is using a self-signed ce
The info you provide is very little as well as your stack trace.
I'll take a guess here.
What I suspect is that in the new server the protocol is TLSv1 while your clients try to connect with SSLv3 (or less) and as a result the handshake fails.
Change you clients to use higher version of TLS
or
Make your webserver support SSLv3 as well. I know how to do this in Tomcat but not in JBoss.
If this doesn't work update the post with more info (and a full stack trace).
You should enable ssl debug info -Djavax.net.debug=ssl