Attempting to "burn" it away has limited success. If you have one dead pixel it's always possible you can get more. At that point, many people who are deep in to monitors consider the screen toast. If you fight with HTC (or whichever carrier) you can likely convince them to send you the replacement first, along with a mailer to send the old phone back. I know for HTC to
repair the phone, they want it sent in (obviously), but to just do a RMA on it you can probably convince them to send you a new one first. Just use a line like "what am I supposed to do without a phone for these weeks while I wait for the new one". Or you convince them to overnight it if that doesn't work. Usually they're flexible enough to do that if you try hard enough. I've been able to pull it off with LG, Samsung, and HTC before, as well as with T-Mobile's Insurance Program for repairs, so give it your best shot