Changed out battery to new one now car will not start with key but can jump solinoid and start 97 sunfire 2.4l

Take a volts reading off battery with multi-meter if low take battery off and re-charge or try new battery.

Is your battery/connections any good?

How about the start solinoid? Try jumping the large terminals with a large screw driver and see if it turns over if so make sure there is 12 volts on the coil of the soinoid when you turn the key, if so replace the solinoid.

solinoid for starter is bad. on a lot of fords the solinoid is mounted on fender, under hood. if you jump from one side to other on solinoid, and it tries to start then solinoid is toast. just follow the positive cable from battery. and you will find it.

yes, wire or switch. Trace back from the solinoid until you get the 12 volts the solinoid should get with key in the "start" position.

check for corrosion/ battery may need replacing

I have this problem right now also. Here is the deal as I see it. I have a 97 Saturn SC2 automatic (nuuf said!).
Against my intuition I let the guy at Autozone talk me into a battery, though I suspected the solinoid or the starter motor itself.
Put in the new batt and nothing but a single loud click. I took the new battery back and used the refund money to get a new starter.
I put it in and still just a loud click. I have cleaned the terminals and torqued the cable at the batt and starter.Because the solinoid clicks when I turn the key I am asuming (for now) that the ignition switch, neutral saftey switch and the "Startguard" (the little electric key you have to put in for your car to start) is good. In my knowlege, it has to be the main battery cable that runs from the battery to the starter. Next I'm gonna go out there and turn my key to the on position and connect a jumper cable from the battery directly to the starter solinoids high current side to confirm or bust my suspicion of the bad positive (red) battery cable. I will let you know how it goes.

Its likely that you have either a bad ignition switch or a bad neutral safety switch (if stickshift, clutch switch) Try starting in neutral...if it starts, change neutral switch (jump across clutch switch, check starting in neutral with your foot on the brake) Ignition switch is on top of steering column under dash.

If the car would not turn over with the key but did start by jumping the solinoid, I would change the solinoid. Even if the car died after you did this the solinoid could be the culprit since it sends power to more than just the starter. Cant gurentee it, but I think thats your problem.

The problem is either the starter solinoid (located on fender near battery) or you are not getting power to the "s" terminal on the starter solinoid from the ignition switch. If you follow the positive battery cable from the battery you'll follow it to the solinoid. Remove the small wire from the terminal marked "s" on the solinoid and using a screwdriver jump from "s" terminal (not the wire) to where positive battery cable connects to solinoid. (with battery connected). If starter doesn't do anything the solinoid is bad. If starter cranks then you are not getting voltage from ignition switch through "s" terminal wire.