First thing to try is just resetting it with the in-set button on the back.
If you've just bought it, do you know what firmware it has on it?
Some of the earlier firmwares are notoriously prone to this sort of behavior.
When you turned it on previously, did it have a greyscale pattern? If so, you're definitely going to want to update the firmware.
You can find the latest firmware and instructions on how to download and install it on the page
here. You'll need an SD card to do this.