You didn't uninstall Java properly. Try again, carefully following the steps.
1) Uninstall all versions of Java from your computer.
2) Verify that you removed all Java versions successfully. You can do this by pressing Windows + R and then typing "cmd" without the quotes. Then type "java -version" without the quotes. You should get the following error:
'java' is not recognized as an internal or external command,
operable program or batch file.
If you do not get that, then you did not uninstall Java properly. Go back to (1).
3) Do
*not* install Java.
4) Install and run RuneMate.