My PC won't boot up into windows. I've booted with an Ubuntu live CD and able to backup my most important information.
Is there a way I can backup my Outlook 2007 emails?
You can back up the PST file which is where Outlook stores its data.
In Windows XP, The file should be in C:\Documents and Settings\\Local Settings\Application Data\Microsoft\Outlook
For Vista and Windows 7, the file should be in here: C:\Users\\AppData\Local\Microsoft\Outlook
It's important to note that these are only the default locations, and it is possible for the file to be located anywhere on the system. But unless you changed it yourself it should be in one of these locations.