I'm having this issue too, and moving around the location of the kunenalatest module did not help. However, I believe I've isolated the issue (not the reason behind it, just the issue
).
I saved two static versions of my page. CB's facebook plugin was active in both. mod_kunenalatest was INACTIVE on one and ACTIVE on the other.
I then ran a diff between the two files to isolate the differences. I found the following important difference: When mod_kunenalastest was active, CB's facebook module doesn't appear to correctly inject its javascript into the page. As a result, the associated login button does not function (and there are no javascript errors to report).
Just to make sure, I copied the associated javascript from the "working" pages to the "not working" page, and the Facebook connect button appeared to work (since this was a static page, I never completed the operation, so I don't know for sure).
Any other debugging efforts really didn't yield any fruit -- when I turned debugging on, I got several hundred lines of sql queries, but no errors.
Perhaps this insight can shed some light on the source of the problem, however.