You need to figure out if you have wax on your floors or a poly finish. It's probably the latter, but here's how I would tell: take some dish soap and scrub floor in a small out of the way spot. Wax will come up, poly won't. (Rinse with dilute white vinegar to remove the soap stickies.)
You'd have to re-poly to make them shiny again, unless it's just a dirt problem (while this is unlikely, you could always try to clean the high-traffic areas first).
Parenting two active, wonderful boys
This is your world. Shape it or someone else will. -Gary Lew