I have a feeling the systems due to its age and what seems to be onboard video are just not up to the task. Even with minecraft looking like a very basic game, it has lots of things to draw since a wall is not made of a simple mesh, but instead of MANY blocks.
This may not be the answer you want, but it is kind of like wanting to play <Insert favorite new console game here> on Nintendo 64, its just not going to happen.
Start>Control Panel>Java Icon> Java tab> Click on view> under parameters add xmx512m> save settings and then run minecraft <-- you can change the 512 to whatever memory you want to give to minecraft. i do 1024.