You can't get into Cisco ASDM and get "Unable to launch the application" from Java. Here are ALL possible ways to resolve this-
1) Make sure you are on the latest ASDM (7.x). You don't need to upgrade the OS to run the latest ASDM.
2) Go to control panel, java, click on the security tab, click edit site list, and add the URL to your Firewall. Make sure you include "https://"
3) If that doesn't resolve it, make sure 3des is enabled in "show version" on the ASA.
4) If it is, issue these commands-
ssl server-version any
ssl client-version any
ssl encryption rc4-md5 rc4-sha1 aes128-sha1 aes256-sha1 3des-sha1
ssl certificate-authentication fca-timeout 2
5) If that doesn't work, issue these. Use your own username and password.
aaa authentication http console LOCAL
username cisco password cisco