The Games
Before looking at the console as the source of your troubles, start with the game you are trying to play. Make sure the game has been fully inserted into the console. Improperly placing the game in the NES will prevent the console from reading the game. Turn the game over and blow into the bottom of the cartridge to remove dust that has accumulated. For a dirtier game, take an eraser and gently rub it against the metallic connector inside the bottom the the game, then blow out any eraser shavings.
If you're still having trouble with the game, apply a small amount of cleaning solvent, such as glass cleaner, onto the end of a cotton swab and rub it against the metal portion of the game. When you remove the swab, you should see it has been coated in dirt. The game should now be playable, but if it still doesn't work, your console may need cleaning.
The Console
If, when you turn on your console, the power light flashes and an image blinks on and off your television screen, there might be a problem with your Nintendo, not the games. This may occur when the game has not been inserted fully into the system or the connector within the system is dirty. You can blow inside the console or used compressed air to drive out any loose dirt. If you are still seeing issues after these attempts, you will have to take apart the console to clean the inside. See the Resource section below for a guide to cleaning the NES.
For power issues, make sure the power cord and television adapter are properly hooked up. If, when you press the power button of the NES, a light does not come on, you will need to replace the power cord. The television adapter should also be tightly screwed into the outlet on the back of your television set, as a loose connection will cause the image to disappear.
Goodbye Game Saves
Before memory cards and hard drives, games featured internal batteries that allowed data to be saved directly to the cartridge. Nintendo games such as "The Legend of Zelda," "Dragon Warrior" and "Final Fantasy" all featured this internal save feature. Twenty years later, the batteries in these games are beginning to die. If your saved game vanishes the next time you pop in the cartridge, this is the reason why. The batteries inside games can be replaced, but doing so will erase any save data you currently have stored on the game. See the Resource section below for a guide to changing batteries in NES games.