I have a 2008 Chevy Malibu four cylinder 2.4 L the battery tested good brand-new starter but I am still getting a no start no crank. I have full power in the car but when I turn the key everything dims until I release the key. I have tried the neutral safety switch trick I tried the antitheft trick of turning the key to accessory for a while and then off and then trying to start my connections all look good I've checked all my fuses and my relays. He problem began when I replaced my battery due to corrosion. Ever since then I've had a no start no crank. I'm fairly handy with cars but this one has me scratching my head. The only thing I can think would be ignition switch or possibly corroded positive cable from the inside that I can't see. Any additional ideas would be appreciated. Thank you.
I think you are correct about the bad positive cable (or the negative cable). There is obviously a bad connection that is causing a voltage drop when attempting to draw a large current, which causes the lights to dim.
The connection between the cable and battery terminal connector on either the positive or negative cable may be corroded. It may even be as simple as the connector needs cleaning where it touches the battery terminals.
If there is no fault at the battery terminals, also check the other end of the cables.