Comment 4 for bug 196858

After X fails to start you should be given a warm and welcoming console connection. If not, press Ctrl+Alt+F3 to switch to another console connection.

once you are at the console you have a myriad of options, you could start an SSH, Telnet, FTP, or heck, even an HTTP server and pull the files off the computer. Or you could use command line sendmail to e-mail a file to yourself and copy and paste on another system. Be creative, the console is not scary at all, and if you need any help, just google or ask.