What is showing on the screen? Is it fully charged? Has it been dropped?
1. Charge it fully. If there could be any question about your microUSB cable, try a different one.
2. Try a paperclip reset
3. If that doesn't work, try a factory reset. Hold the power slider for around 20 seconds to make sure it's off. Hold the Home button down, and slide the power button (quickly, don't hold).
4. If that doesn't work, repeat 3.
5. If repeating 3 doesn't work, try it again, but instead of holding Home and sliding the power button, hold Home down and press the paperclip reset.
6. Repeat 5.