openjdk shouldn't be a problem. I've been using the two together since Fedora 10.
1. Has you ever been able to run eclipse on this machine? If so, what do you think might have changed?
2. Did you install eclipse using yum?
3. Try moving ".eclipse" and workspace (default "~/workspace") directories. This will remove any eclipse plugins you've installed as well, so make notes on what plugins you want to reinstall. This will force eclipse to recreate these directories and maybe resolve your problem.
Code:
$ mv ~/.eclipse ~/.eclipse.old
$ mv ~/workspace ~/workspace.old