Do you absolutely have to use some kind of glue or sealant? Why doesn't that video on laptopscreen.com show putting glue back on? Is it just a personal preference?
Well keep in mind that mine was a VPCEB, not a VPCEA, so there may be some slight differences. They're the same line, but yours is 14 inches and mine was 15 inches.
Anyhow, the glue is not absolutely necessary for the repair, but I highly recommend it. In the case of the VPCEB, the plastic "snaps" were too far apart to keep the plastic from bowing out away from the LCD frame. It looked horrible, but it was 100% functional.
Basically, the design looked like this on the left and right sides of the front bezel:
Screw [3 inches of nothing] plastic "snap" [3 inches of nothing] screw
The bottom looked similar:
Screw [4.5 inches of nothing] plastic "snap" [4.5 inches of nothing] screw
Those "inches of nothing" portions originally used glue to hold them against the LCD frame. When you remove the bezel, most of that glue loses too much of its stickiness and stops actually working. If it doesn't stick, it just bows out and looks terrible. It even rubs against the bottom half of the laptop when you open/close the lid.
Solution? When you remove the bezel, scrape/peel off all the original glue and replace with your own, new glue. The glue is $3 to $5 at any car parts store
🙂