Engine whirrs and clicks, but still won't start?

I have a 1999 Ford Escort that suddenly just stopped working. It won't start. When you turn the key, it whirrs and makes a clickity-clickity sound, like it's trying to start, but the engine won't actually start up. I've tried changing the spark plugs and the fuel filter (a friend of mine thought that might be the problem), but it's made no difference. More recently, when I try to start it up, it will whir and click for the first few tries, but after that it stops making any kind of noise at all. What on earth is wrong with my car?