Since there's a conflict between the latest Chrome and Speed Dial (I've logged the issue with the entension author via the Chrome web store), only on https pages, I've found this work-around.
I located the directory where Speed Dial installs to (thanks @Synetech). On Windows XP should be something like:
C:\Documents and Settings\[My username]\Local Settings\Application Data\Google\Chrome\User Data\Default\Extensions\dgpdioedihjhncjafcpgbbjdpbbkikmi\2.5.1_0\images
Although there were no thumbnail images in this folder, I created my own folder under images entitled "mine": ..\2.5.1_0\images\mine
I then copied a screenshot I'd taken using Google Screen Capture into this directory as "trello.png".
The last step was to go to "Edit Dial" and type "images/mine/trello.png" into the "Dial Image URL" box (you can also load images from any url such as photobucket).
Clicking save then immediately displayed my screenshot as the thumbnail.