I'm scratching my head as to how your old saves can be on your new computer, when you say that you previously installed and played the game on a different machine. The only way the saves could be transferred is if you transferred them manually -- which you apparently didn't do.
When installing a game on a different
machine, old saves are not transferred.
Some games come with preinstalled saves. Evil Under the Sun is one example I can think of.
Did you try running a file search as MaG suggested, to try and find the save location?
In the majority of cases, starting a new game will not delete existing save files.