Hey there,
The old computer that you say still has your pics on it's hard drive, what was wrong with it, was it a hardware issue with the HD itself, or something else with the computer? If it was something else, then the drive is still good and you can get the data off just by adding it to your current machine as a slave drive and copy it over (if they both use the same data bus ie SATA or IDE). I work with computers for a living, let me know if you need help and I can try to help you out.
-Mike