Widget code not visible in TwentyTen theme

I’m wanting to copy and paste the code in my widgets into a text editor, so I can change to a more recent theme. I’m using a child them (Responsive TwentyTen) of the TwentyTen theme.

However, probably due to some recent core update (3.8?), in Appearances / Widgets it just shows the widgets and their titles but when I click on the Edit link next to the widget name it only shows the position number of the widget in the sidebar. I can no longer access the code with all the links, etc. of four of the seven widgets I’m using.

The widgets still display correctly on the site but I’m can only get to the code of three out of the seven (likely ones created with the Text widget. (www.newcreationrealities.com)

Any ideas? Any way to reinstall an older core version (like say 3.6 or whatever) and extract them that way? Or how do I find them in the database?

Thanks, Peter