Old Carpet on Stairs - Loose and "slick" ?

I know that carpet is usually the safe option for stairs, however... the carpet on our house is really old - about 11 years now, and is what I would guess to be builder's grade carpet? It gets pushed down to where the threads lay flat, and when that happens the carpet gets "slick". It doesn't help that the carpet is loose on the stairs too. I was considering getting the carpet professionally cleaned and stretched, but to be honest, I have no idea how much that would run me, or even if it is worth the money. I have some money saved up that I was hoping to spend to put hardwood in my living area and dining room, but these stair conditions are hazardous! Anyone know a sure solution to this issue or should I just look into getting the carpet for the stairs and upstairs replaced? Any recommendations for a good carpet for the stairs and upstairs? Preferably one that doesn't need to be vacuumed every time someone steps on it to keep it looking good.