Hi!
As you suggested, that line is indeed a sign of a loose connection. If your monitor is still under warranty, then don't bother dismantling it yourself, Dell should fix that, even if you lost the warranty slip. You just need to find the Service Tag on that monitor (Dell has a video on how that's done: http://www.dell.com/learn/us/en/05/videos~en/documents~esupport-find-your-monitor-or-projector-service-tag-eng-v1.aspx ) and then type it into their support website. Then you'll get more options, one of them should be warranty & repairs or something like that:https://www.dell.com/support/home/us/en/05/products?~ck=mn