Intermittent issue of engine not cranking?

I drive my car for a while, park it, and then come back to it, the key would turn all the way, all the electricity in the car would come on, but the engine wouldn't crank over. I noticed the past few times if I waited 10-15 minutes I could get it to crank and I'll be on my way, or if I was lucky enough I turn the key all the way and hold it and then it would crank. The keys are old, I notice I have to get close to the car to even unlock it, so maybe it's the key, I'm not too sure. Haven't checked the starter yet but will very soon. Please help me.