Try this:
1. Check your cables and make sure they are firmly plugged in,
2. Try pluging your xbox 360 slim into a differant T.V
3.Try removing your Hard drive and playing without it
If all other Fails and you cannot figure out your problem then you need to get your xbox repaired. From what it sounds like: If you bought your Xbox 360 slim Console Brand new, You should still have a warrenty
Hope this helps
-Sage