As the others have said, you can't use the track without permission. And you're unlikely to get it as it's for a commercial product, and the use of the song suggests endorsement. I'm not sure why you'd say it's "not for profit." If you're using the song to promote your business or product, it's for profit.
While it's great to use a popular well-known music, it takes only a little more effort to find local bands with similar music. Ask for permission, and give credit (in the video, and in the YouTube description). They often will allow it at no cost for the promotion they get. It also helps to drive traffic to the video, because they'll Tweet or blog about it. You can bet Lady Gaga isn't going to mention you've copped her latest song on her Twitter account.
While it's great to use a popular well-known music, it takes only a little more effort to find local bands with similar music. Ask for permission, and give credit (in the video, and in the YouTube description). They often will allow it at no cost for the promotion they get. It also helps to drive traffic to the video, because they'll Tweet or blog about it. You can bet Lady Gaga isn't going to mention you've copped her latest song on her Twitter account.