I believe nowadays you can e-mail videos as an attachment to a unique e-mail address that facebook assigns to you. Then it should automatically appear as one of your videos on facebook. Try logging into facebook and looking for this personalized e-mail address.
@SmoothRt is correct you need your personal FB email addy to upload videos
I am unable to post the link to the FB page that describes how to find it as I haven't posted here before so here is the copy:
You can use your personalized upload email address to email a photo/video from your computer or mobile phone. The uploaded content will then appear in your Mobile Uploads album.
To see what your personalized upload email is, please take the following steps:
1. Go to your Publisher, located at the top of your Wall, and click the Photos button next to "Attach."
2. Select "Upload a Photo."
3. Click the "upload via email" link.
A dialog box will appear with your personalized upload email and further information about using this feature. Be sure to save your upload email address as a contact for easy access.