Hello,
After debugging the site for almost the entire day, it looks like this issue is caused by SH404's plugin. For some reasons they are actually generating the fb-root tags as shown here,
http://screen.stackideas.com/2015-03-30_0111.png and this tag actually messes up Facebook's renderer script. I have no idea how to turn this off in Sh404 and the only way I did to test this is to rename their plugin files and these codes are no longer generated.
To reproduce this, all you need to do is to rename the following 3 folders to another name and you'll notice the button appearing fine.
/plugins/system/sh404sef
/plugins/system/shlib
/plugins/system/shmobile
I have also even tried copy / pasting the codes Facebook provide on non easyblog pages and they wouldn't appear as well until I rename SH404's plugin.