Symptoms

K2 blackpearl for SharePoint page not being displayed properly (looks like CSS was not applied correctly and/or some images are not accessible).
 

Diagnoses

This issue may happen due to the fact that the following documented requirement hasn't been met:
http://help.k2.com/kb001692

"If there is a second site collection on a Web Application on a SharePoint on-premises environment, the K2 App will have a dependency on a Root Site Collection. If there is no Root Site Collection or the existing Root Site Collection is deleted the K2 blackpearl for SharePoint page will not display correctly."

Please note that Root Site Collection not only have to exist but also has managed path configured so that it is reachable otherwise you will get the same problem.
 

Resolution

Create a site collection at the root level of the SharePoint web Application and make sure that SharePoint managed paths configuration makes your root site collection reachable.