Got bit by this on my personal servers in the past week. A very helpful post pointed me to the issue:
https://melcher.it/2014/02/sharepoint-2013-cu-august-2013-internet-information-services-installed
Except…mine was a tad bit different. The IISADMIN service was completed removed from the WFE! This was due to a SharePoint Server windows update not completing and failing. In order to get it back, I simply re-ran the pre-req installer and once the service came back, I was able to load the Central Admin and continue with windows updates.
Enjoy,
Chris