I figured it out. When I downloaded and installed the latest Java version via Apple, it actually installed multiple versions: 1.5 for 32-bit machines, 1.5 for 64-bit machines and 1.6 for 64-bit machines.
Under Macintosh HD > Applications > Utilities > Java Preferences, these multiple versions are listed in order of preference, ie, the OS will try to run one particular version first. In my case, 1.5 32-bit was listed as the default. Switching to 1.6 64-but fixed the problem.
Thanks for your help everyone.