Engine won't crank over

Left work and car was driving fine, no problems at all. I stopped to get gas and when I went to crank back up, all that happened was a rapid series of clicks. The lights, radio etc still came on but car wouldn't start. Waited a few minutes and tried again w the same result. Popped open hood, cleaned battery connections, made sure they were secure and tried again. This time lights etc didn't even come on. Tried to jumpstart car. Lights etc returned, but still just a clicking noise without engine turning over at all. Left my car on cables for 10 or so minutes while other SUV revved engine, still just clicking. After about 30 minutes we gave up. As soon as my Tucson was unhooked, lights dimmed and went out. Not even enough power to auto lock doors. Had to do them manually. Is this just a battery problem, and if so why did it die out if the blue with no warning. Or is it something more serious? Could my starter/alternator be messed up?