On the SharePoint 2013 server running the User Profile Service Application you see three errors in the Windows Application event log:

Event ID 1015

Failed to connect to server. Error: 0x80070005

Event ID 1004

Detection of product ‘{90150000-104C-0000-1000-0000000FF1CE}’, feature ‘PeopleILM’, component ‘{1C12B6E6-898C-4D58-9774-AAAFBDFE273C}’ failed.  The resource ‘E:\Microsoft Office Servers\15.0\Service\Microsoft.ResourceManagement.Service.exe’ does not exist.

Event ID 1001

Detection of product ‘{90150000-104C-0000-1000-0000000FF1CE}’, feature ‘PeopleILM’ failed during request for component ‘{1681AE41-ADA8-4B70-BC11-98A5A4EDD046}’

In order to resolve these errors grant the Network Service account read access to the Microsoft Office Servers\15.0 folder.  By default this is in %programfiles%, but may be one a different drive if you chose to install the SharePoint files to a different drive.

If you encounter the error for event ID 1015 on servers not running the User Profile Service Application, then add the SharePoint Farm account to the local administrators group and restart the SharePoint Timer Service.