HELP 3 week old MacBook Air with black screen

Hello Nelly1964,

It sounds like your computer will not turn on at all. I would like to recommend the troubleshooting in this article named:

Troubleshooting: My computer won't turn on

http://support.apple.com/kb/TS1367?viewlocale=en_US

If your computer won't turn on, try each of these steps:

1. Verify you have a good connection from your Mac to the wall outlet by confirming the power cord and adapter if present are securely connected and plugged in. To check if the wall outlet is working, plug in a lamp or other electrical device.
2. If the wall outlet is working and you continue to have no power try another power cord or adapter if available. If it works you may need a replacement cord or adapter.
   Note: See Apple Portables: Troubleshooting MagSafe adapters for further troubleshooting with MagSafe adapters.
3. Disconnect all accessories that are plugged in to the computer, such as a printer, hub, or other mobile device.
4. If your Mac supports user-installable memory, solid state drive, or hard drive, and you recently installed any of these, make sure they are installed correctly and are compatible with your computer. If possible, reinstall the original memory or drive into the computer to find out if the behavior persists afterwards.
   • MacBook Pro: How to remove or install memory
   • MacBook: How to remove or install memory
   • Mac Pro: How to remove or install memory
   • Mac mini: How to remove or install memory
   • iMac (27-inch, Late 2012): Installing or replacing memory
   • iMac: How to remove or install memory
5. Reset the SMC.
6. If you are still unable to start up your computer after trying each of these steps, visit an Apple Store or Apple Authorized Service Provider (AASP) for further diagnosis. If you plan to visit an Apple Retail Store, make a reservation at the Genius Bar using http://www.apple.com/retail/geniusbar/ (available in some countries only).Note: Diagnostic fees may apply for issues not covered under warranty or the AppleCare Protection Plan (APP).

Thank you for using Apple Support Communities.

All the best,

Sterling

Have you tried doing a hard reset - hold start key down for 5 to 10 seconds. If it chimes and restarts, you should look up Black screen freeze after sleep or similar here on the forum for lots of info (not a solution yet regrettably).