When should i change the snare on my snare drum?

I bought a piccolo snare drum from my cousin, and I was spending today tuning the snare. Despite tuning the snare tightly, the drum still has a sloppy sound when I hit the drum. It just does not sound like the snare is pressed up against the head of the drum. Does the snare need replaced? I've fooled around with the drum for hours, and that's the only other thing that I can think of as to why it sounds so horrible.