Change old battery out now car won't start

Check the alternator and the electrical system if that's not it.

It may be a bad starter, among other things.

Does the engine turn over, or do you hear clicks when you turn the key or push the start button?

Would it start before you replaced the battery? Will it start with jumper cables?

It could be any manner of things, dodgy alternator, dodgy starter motor, frayed leads, damp/broken points. Check your connections, clean your points and distributor cap, use WD40 to get rid of the damp.

As a rule it takes a lot more power to turn an engine over than sound a horn or turn on a light. Your battery may not have enough charge, or it might be dry. Have you checked to see if it needs topping up with distilled water?

Do that first.