You're good, use the stuff you made the starter with. When I'm motivated I try to wash my yeast really well and leave it in the fridge. Take it out to warm up a few hours and you're good. Granted, you have a starter's worth of unfermented starter but the yeast is fine. To me, it's about getting enough yeast in there. If you made a starter a day ahead of time and your fermentation starts quick, rock on, but otherwise it'll be just fine.