Want to get involved in developing SMF, then why not lend a hand on our github!
One issue I see is guests don't have permissions to view attachmentsSo you can't see the images as guest on a forum such as http://www.tseatc.com/smf/index.php/board,25.0.html
When you moved servers, did you use FileZilla to download the attachments?
But this mod uses attachments, are you using that icons folder for all attachments to posts?
sounds like you are actually using this modhttps://custom.simplemachines.org/mods/index.php?mod=511
it should work just fine.... I suspect that your images are in the wrong location. Ask in the support thread for that mod.