It only takes a few wet rides (or car trips with bike on rack) to have water find it's way up and into the headset bearings. Once there the water won't evaporate quickly and the grease will be contaminated, rust follows.

That your headset sounds to be both loose (the faint play) and yet tight (the not turning with the bike leaned to one side) speaks to the possibility that the bearings are in bad shape. But without my telescopic and x-ray vision (sorry I leave those eyes at work) I can't say for sure. Andy.