I'm using Adobe Acrobat X Pro and have been following the procedure :
1) open PDF,
3) Multimedia dropdown,.... but then the 'Video' button is not live.
Why is that because I'm trying to add a video to my PDF?
As per the description above, you are not able to add video in a PDF file using Acrobat Pro 10, Is that correct?
Please refer to the following KB docs which discuss the similar scenario Adding multimedia to PDFs
Note: Acrobat Pro 10 is already declared as End of Support product, End of support means that Adobe no longer provides technical support, including product and/or security updates, for all derivatives of a product or product version (localized versions, minor upgrades, operating systems, dot and double-dot releases, and connector products). For detailed information, refer to End of support for Acrobat X and Reader X
Feel free to update this discussion in case you need further assistance.