Those machines should be fine - if you're willing to sacrifice the Arduino IDE, just about any computer would work as well. The OpenJDK works well for me, and there have been some problems (on this forum) with the Sun Java binaries. If you're using the Sun binaries, try using update-alternatives to switch to the OpenJDK.
Unless you've got a good reason not to, you should probably update the install to a recent distribution - unlike Windows, linux updates rarely require more resources as compared to older versions. Ubuntu 11.04 is nice (Unity notwithstanding), and it has Arduino prepackaged - that would do the setup for you, and should fix the java errors.