I had the same problem, but the prior answers require an unnecessary amount of file-fiddling. While setting up a new laptop which came loaded with Win 8.1, like many experienced computer users, I immediately loaded in the most essential programs first, such as Windows Live Essentials 2012. And Live Mail worked fine initially. However, after several days reloading less critical applications, I eventually developed the exact same problem mentioned above: WLDCore.dll suddenly went missing. I'm not sure if the registry got messed up or whether a critical folder was overwritten or deleted by a pre-Windows 7 or 8 program being installed.
As of 2012 and beyond, this problem is most easily resolved by going to:
(1) the Control Panel*,*
(2) select "Uninstall a Program",
(3) scrolldown to "Windows Live Essentials 2012",
(4) right click on that selection and select "Uninstall/Change".
(5) The first dialogue box will give two options**.** Select**"Repair All Windows Essentials Programs".** After 5 seconds, Windows Live Mail (and presumably all other of its programs) will function normally again**.**I'm not sure if the uninstall program off-loads the necessary files from the web or from a local disk store of the files, so you may need to connect to the internet to do it. Perhaps a tech can provide some clarification on that point.
This works with Windows 8.1 and I would imagine any other version of Windows that could have initially run the Windows Live Essentials 2012 setup. Going to the "Uninstall a Program" control panel is not an intuitively obvious place to fix something without uninstalling it, so I thought I'd mention this easier option.