MacBook – The Apple light on the Macbook is damaged, could this damage the screen

I'm surprised no else one has said it yet:

This is a nearly brand-new MacBook Pro still covered by warranty.

There is absolutely no reason that your keyboard keys should damage the display like that. This is a design flaw that has existed in their laptops at least as far back as the PowerBook G4. The keys should not touch the screen when the lid is closed under any circumstances, but they invariably do.

I have to clean my screen every few days to get rid of the keyboard imprints, but luckily have taken no damage to the screen (probably only because I use the awesome Moshi keyboard cover, which also saved my MBP from a hot tea disaster).

Take it to Apple and make them fix it under warranty!

Yes - the SMC reset should resolve any temporary issues with the hardware not sensing the charge adapter. It's even called out in this KB article by Apple as something SMC reset can potentially address:

http://support.apple.com/kb/ht3964

Once you ruled out SMC needing to be reset, you should get the Mac in to a repair shop or do what they would do to isolate the hardware failure:

• test your adapter with another computer
• test your computer with another adapter
• test your computer with another OS (last resort - SMC and the charging behavior you report can be tested with the OS powered off and only the firmware / SMC regulating the LED color and charge state based on the data it can collect which is faulty in your case)

Once they have isolated the failure (likely to your computer), they would open it and inspect for any corrosion or damage on the logic board and charging circuitry and the either swap and test the magsafe board or the battery or the logic board itself based on experience and the hardware service manual for your model.