The most common culprit for this is usually that the Javascript Valid SDK Domain is set incorrectly in your LinkedIn application. You can see instructions in our
LinkedIn Application Setup Guide
on how to set this properly. There's usually a javascript error in the console when this is the case, but since I didn't see any evidence of the LinkedIn button at the
link you provided
, I can't tell you if that's the cause. If you disabled the module, then please try re-enabling and checking the value for this application setting.
-Melissa