If you edited the CSS using the custom css panel in admin panel then you should just be able to update the theme it was based on. If you made any hard code changes then I can only assume, remake the theme and test with your custom edits.
Comparing changes in your theme and default theme from 1.3 would help. Use any merging tool like Araxis Merge to see what parts of code should be modified to make your theme compatible with the 1.3. version.