What is your Reader XI version? If less than 11.0.07, try installing that latest version from http://get.adobe.com/reader/enterprise/
The "failed to load its core DLL" message usually arises due to some rootkit malware; if TDSSkiller was unable to resolve that, I don't know how to proceed further.
Last idea: try disabling Protected Mode via the registry: download, unzip, then run the registry script from https://files.acrobat.com/a/preview/d73de11e-df84-4f32-b803-0bf53bc12259