In this case if you have confirmed the pixel is indeed dead and you cannot massage it to life again; just face fact and prepare to either send it in to Nintendo for a repair or replace the unit. I'd recommend a repair if you've still got any warranty left; this is usually a One Year Limited Warranty that would normally cover such things as dead pixels. It may take a few weeks to repair or you can just have them advance replace the unit if you've got a Credit Card which can authorize a temporary hold of about $300 USD. (This hold is released when they receive the broken unit, this option has a fee, not sure what it is nowadays.)
Keep in mind this advice is given based on my experience with the policy of Nintendo of America. Other regions of Nintendo may observe differing policies based on local laws in your country or the country of operation.