I would request you to please uninstall and reinstall Quick Time Player.
Please let us know if it helps.
I have the same problem but I am using Windows 7 Ultimate SP1.
First I was having issues just to import, the lightroom freeze if I tried to import more than 10 or 15 images at a time.
I solve that issue by downloading the "dvamarshal.dll" file and coping it on the folder of Lightroom,
I manages to import and create a new cataloge with 119629 photos but then it didnt import any video, no matter if its a mgpe, mov, mp4. It just says is doesnt support video, enable video mode. ""Video support is disable"
I didnt have Quick time install, so I did install and uninstall it. no change, still dont recognize any video files,
Any solution available?
Could you please let me know the exact version of Lightroom installed on your computer?
Make sure to update Lightroom to the latest version CC 2015.6.1/6.6.1.
I am using Versión de Lightroom: 5.7.1
Sistema operativo: Windows 7 Ultimate Edition
Versión: 6.1 
Arquitectura de la aplicación: x64
Arquitectura del sistema: x64
Cantidad de procesadores lógicos: 8
Velocidad del procesador: 3,4 GHz
Memoria incorporada: 31970,8 MB
Memoria real disponible para Lightroom: 31970,8 MB
Memoria real usada por Lightroom: 1665,6 MB (5,2%)
Memoria virtual usada por Lightroom: 1634,7 MB
Tamaño de memoria de caché: 1275,6 MB
Número máximo de subprocesos que usa Camera Raw: 8
Ajustes de PPP del sistema: 96 PPP
Composición de escritorio activada: No
Pantallas: 1) 1400x1050
When you said that "make sure I have the latest version"... you mean that I HAVE TO SPEND MORE MONEY because the product I have is not working properly and your solution as a customer support is to make us buy something new?
If thats what you are sugesting, you are not helpfull at all. and if I have to buy a new program for sure it will not be an Adobe product, cause it means you are selling products that do not work, your support department does not make honor to the name and should be rename as SALES DEPARMENT FOR FOOLS and you just want to make money.
So please, if you have any solution to REPAIR my actual program, please tell me how. And I really dont understand how a company like yours, have not address this issue that has been happening for quite a while now and to a lot of people for what I am finding in different forums.
Hoping to get a reasonable solution, yours
Thank you for the information Roberto, I thought you were working on the latest version of Lightroom.
You don't have to purchase Lightroom 6.
From which location are you trying to import the videos?
Also install the latest version of Quick time player on your computer.