You're out of luck if you don't have an install disk or file.
But that probably wouldn't be the real issue anyhow. If you are getting a new computer with a modern OS (like Vista), Acrobat 6 won't run on it anyhow. You would need to upgrade.
would an install file have been added to my computer automatically do you think? I could have a look for one if you're able to point me in the right direction for it?
Unless you downloaded the file from the web store, you won't have it.
But again, 6 won't run on a modern OS. I'm also not sure if it even qualifies for an upgrade so be prepared to pay for the ful version of 9. If it DOES qualify for the upgrade pricing, you'll still need the serial number for the old version. If you registered it with Adobe when you got it, they may be able to help you with that.