In my basement and half of my living room the electric is not working and the breaker is not tripped... where do I look for the problem... we already put in a new breaker in the panel for this area

A short in one of the outlets between the panel and the room?

Well it is all of my basement and 3 outlets in the living room we are thinking running new wire? Is that all we can do?

Logical place to start, check both wires

Start with the first box on the circuit and work your way through the entire circuit. You are bound to find a bad splice, switch, receptacle, etc.

It is an Open, Not a short, or breaker would trip. I would test first bad receptacle, or last working receptacle in the string. Also check switch box, If outlets from there on are out.