No Power, But Headlights Come On
 

I have an inline 4 cylinder, DX model. I'm not exactly sure of the year, but I know that it's early 90s. It has not been used in several years. Here's the problem:

I put the key in the ignition, and absolutely nothing happens - no interior lights, no dash lights, no beeping sound, no anything. If I turn the headlights on, they work fine and are bright (the battery is new and fine), but the hazard lights don't work. I cannot hear the starter solenoid click when I turn the key; I cannot hear the fuel pump working either. For all intents and purposes, it's as if there is no battery in the car at all -- except the headlights come on.

Does anyone have any idea what I should look for? If you can provide relative locations ("driver's side, near firewall", etc.) in your response, I would be very grateful.

Thank you.