BEST BUY Brakes in less than 2 weeks, claims my fault Internet

Many times if you do, they can and will force a refund/replacement. If this laptop shows no signs that there was any physical damage or pressure applied to the screen, it is your word against theirs. If there is no physical signs of damage other then the white line, it is within reason to assume that this could be a defect.

Not to defend Best Buy but you purchased this online, so of course a Best Buy store does not want to take the hit if Toshiba won't cover it, since it comes directly out of the stores P & L if they replace it and Toshiba claims it was physical damage that is not covered under warranty.

I still say it is not a bad idea to send it to Toshiba since the warranty is with the manufacturer at this point if it is a defect. I can understand a customer may feel Best Buy is not standing behind it's product in this case, but if upon inspection it was determined this is a pressure break, apparently there has to be some evidence. The laptop is covered by the manufacturer so they have nothing to lose unless they replace it and get stuck with a damaged laptop that the manufacturer will not cover.

A sticky situation yes, but if corporate yields no positive result, the only hope you have is Toshiba will take responsibility for if being a defect. If they find any signs that the screen was damaged from pressure, chances are good they will not warranty it, but as I stated earlier, it is worth a shot since if this is a defect, it is certainly covered under warranty after only a couple of weeks.

It's a 14-day return policy on laptops. Also, have you ever closed a laptop with something like a pen or even something smaller sitting on the keyboard? That tends to break a screen without any damage to the case. Toshiba cases are typically plastic and plastic is FLEXIBLE. You don't have to leave a mark on the outside to damage the inside. Oh, and it's not defective if you buy it and it breaks in two weeks. It's defective if you buy it and it is immediately nonfunctional or shows signs of dysfunction.

It's less than 30 days. Take photos of the defect.  Walk in to best buy and drop it on the counter. Tell them its defective and walk away.
Call your credit card company and tell them you were sent a defective product. You have returned the product and the company refused a refund or replacement.

They will do a charge back to the retailers account. The retailer may try and dispute the charge back, in which case you can send the pictures to the credit card dispute resolution department. Tell them you will not pay for a defective product.

If the laptop had been abused there would be indications on the outside of the case, not just on the screen. The credit card company will see this for what it is. The seller trying to pass off second rate goods.

Have you contacted Toshiba? Since it was only two weeks then the original warranty would be convered by Toshiba and not Best Buy. While BB should probably helped you I would at least contact Toshiba. Another question did you have it plugged into a surge protector? What kind of internet connection are you using? Was there lightning nearby the night it hapened? I have a Toshiba I purchased from Best Buy about 3 months ago and have had no problems.

Now if the screen is damaged, unfortunately that will not be covered..even by Toshiba unless you are very lucky, it's worth a shot.

This kind of line though the screen typically signifies physical damage.

However, it is not the only thing that can cause a line. I would hope whomever checked it for you at the service counter checked for other causes...but here are some suggestions...

Bear in mind, I don't know any manufacturers that cover screen damage, even if non accidental, and a repair may cost close the the original price of the laptop.

Here are a few things you can try however,

See if the lines vary if you pivot and wiggle the screen around.
If the line or lines vary when you do this, it could just be a bad flex cable which are easy to replace and should be covered.
 
Does the line flicker at all? See if it does when you load applications. If so it may be a bad video chipset and that as well would be covered.

If all else fails and you are stuck with it..if the laptop has a an external VGA connection you can use an external monitor. However this would not be convenient if you travel with it.

I hope for you that if this really happened by itself and it is a defective unit, that Best Buy or Toshiba will help you out. Unfortunately, they have to abide by policies however if you get to the right person sometimes an exception can be made. I assume you contacted the Best Buy corporate office. If there is no other signs of physical damage or abuse, and since it has only been two weeks, you may still have hope.

While you were at work is there any chance someone had access to it and could have damaged the screen?

Just because you didn't directly break it, doesn't mean it's a lemon. There's a variety of ways that kind of accidental damage could have occured, but that is the description of a pressure break. Also, neither Toshiba nor Best Buy will cover damage to the screen unless you pay for the Accidental Damage and Handling warranty they both sell. As you apparently did not purchase this additional coverage from either company, you are indeed out of luck. Again, I'm not saying you broke it, I'm just saying neither Best Buy nor Toshiba broke it, and as a screen costs upward of $700 to replace, they are in no way financially responsible for the damage. Perhaps something fell on it in the night or you closed it a little too hard. This is what extended warranties are for.