I need help replacing my bike's tube
Any bike store, and probably any Walmart/Target/etc, will have what you need.

700C (or 650c, 26", 29", etc) is how big around the tube/wheel is, while the x23,28 or x30-42, etc are the width range. You want to find one that, as you mentioned, includes the target size within the range and is a match on size and valve type.

Based on the "replacement" not fitting, I'm thinking your wheel is a 700c/29" and you are most likely looking for the right tube: 700x[range including 35] with a presta valve. That said, if you have a local bike shop, swing in there and the bike mechanic can make sure you are getting what you need. In most cases, the tube is going to cost the same (it's actually cheaper at the LBS I hang at as they buy tubes in bulk and sell them at close to cost) and you will be sure to get the right item.

Bonus: Ask the mechanic if he'd mind coaching you through changing out the tire. Someone who has changed a couple hundred tubes can usually give you pointers on how to roll the tire back on without tools, hot to prevent a pinch flat, and how to make the whole process quicker and easier.