Re: steve anchors reach
You are experiencing weak current to the starter. First thing I would do is to REMOVE and clean (the surfaces that touch each other, not just skim over the outside of the existing connections) every terminal in the loop from the battery red terminal to the engine (usually attaches to one of the solenoid leads on the port side of most engines.....answers that question on location) on to the other solenoid terminal and off to the starter.
Then clean where the starter mounts to the engine block (ground connection if there isn't a dedicated ground terminal on the starter as some engines have). Go back to the battery and do the same on the ground wiring at the battery and back to the engine. While doing that, check the crimp on terminals on the power leads ensuring that they aren't corroded up and if so, replace them......Then...... think about taking a pair of common pliers and jumping across the solenoid terminals to see if it is the problem. Usually they aren't unless the engine has had a lot of starts. The internal terminals arc over when operated and after awhile the arcing pits the terminals thus reducing the surface area of the connection. They touch, but can't carry enough current to start the engine.
Last, it takes from 100 to 200 amperes to start most engines and that takes a battery in good condition and good current carrying conductors. I assume the new battery is fully charged (by you after you got it home) and is equivalent to at least a size 24 having adequate capacity to do the job.
HTH,
Mark