The beauty of patches is that they often can apply even if the code it was generated from has changed slightly.
You can use SVN patches with the standard "patch" utility on Unix-like systems, which has also been ported to Windows (http://gnuwin32.sourceforge.net/packages/patch.htm). This utility gives you a fair amount of control over how the patch is applied and how much "fuzz" to take into account while trying to apply it. Once you've applied your patch, check the svn diff to make sure that all your changes are included and you don't need to modify it any to get it working with the latest code, then you can regenerate the patch so that it applies cleanly.
If the code has changed too much, or on the same lines as you modified in your patch, then one or more "hunks" will likely fail. In this case, the patch utility will tell you what failed, and you can apply those changes manually before re-creating your patch.