The problem is, in 90% of the cases, easily fixable in less than 2 minutes. Open your functions.php file, check the closing ?> and see if there is any extra space after it, especially some linebreaks. Delete any space/line breaks, save and upload the file. Try to publish your page.
Should work again :-).
If that doesn’t work, change your theme to the default theme and see if you can publish. If you can, what you should do next is go through all of you .php files in the theme’s root directory and look for any extra space BEFORE the opening of the documents.
As before, delete all of it and resave. Go page by page. You should have your fix.