As long as the old host hasn't deleted your account, you can change the nameservers back and download what you need.
here's what i did.
i have a wordpress site installed in a host. and i decided to transfer the site to my other host so i chang its nameservers in godaddy and install a wordpress once again.
yet i forgot to download the xml file from the old hosting, can i get it back and will the old wordpress site be intact if i change back the namservers to its old one?
Maybe it's too late for you to try this, but personally I would just throw in your old websites IP address into your own PC's hosts file if you know what the IP address was.. And if your files are still there on your old host you'll be able to access them via ftp or browser etc. Don't leave it too long though, in case they clean it out if you have cancelled your hosting with them already.
Using the Hosts file you won't need to worry about messing around with changing the nameservers back and forward and you also don't have to wait for the DNS to update / propagate.. And this will only affect you, not everyone else too.
If you are using windows you can find your hosts file in:
Open it up with a text editor. Add your old IP address and the hostname/domain name of your website, underneath the localhost line (that needs to stay at the top.)
Once you have the file you need, then remove that line or you won't be able to access your new site anymore...127.0.0.1 localhost
Hope thats clear enough.. If you have already changed your nameservers around, then just keep this in mind for next time.
I use this method to work on (the same) sites that are installed on multiple web hosts. For when I'm planning to move sites, I set it up on the new host first then switch nameservers when everything is ready, or I just want to work on a site without anyone being able to access it, while the exact same site is online somewhere else and is fully available to everyone else to use.