You are likely to benefit the most from purchasing more memory. Only 512 MB means you will have to swap a lot of memory to disk, and the game will be extremely slow. I think that must be the cause of your problems. But it's strange that you should crash on the opening screen, not all that much is loaded by then.

You could also try to run memtest to check whether your memory is error free. Leave it running during the night. If there are no errors detected in the morning your RAM is okay, but still lacking in size to get decent performance.