2001 Honda Civic slow to start - if it starts at all

Recently I screwed up and lost my battery's charge by leaving the headlights on. I jumped it and let it charge up for about thirty minutes, but a few days later it began having trouble starting. It'll choke for a minute, and then usually fire up. For the past couple of days it's been more difficult than usual, and it won't turn over at all if the engine is warm. When it's trying to start, all of the gauges on the dash shiver back and forth, and the indicator lights blink and fade. There's audible clicking from the dashboard that lasts a few seconds after I quit trying to start it.

The battery connections are clean and greased, and the battery itself isn't that old. Could it just be the starter wearing out?