Cant push the button to put in gear

Your clutch disc may be worn out, when the disc wears completely down the pressure plate goes over center and that causes the clutch to slightly engage when the pedal is depressed and you grind gears, most clutches last about 75000 miles.

yeah man this is no big deal mine did that the day i bought it if u look up under ur car right by the driver side and have somebody push or wiggle the button u will c the cable that has come off ur transmission lever which is on the side of ur trany its made of plastic and is a stupid design u can either rig something up to make it stay or have the whole cable replaced cant by just the end like some cables i ended up puting it on with zip ties for a min then bought a little baby c-clamp and that has worked great good luck u can reach down there and put it on enough to get u going or at leat put it in drive to get u home

It is due to be rebuilt

The fluid change didn't help any,
maybe made it worse.

I know you will have issues with my
answer,but I once owned a trans
repair shop

One possibly/likely problem is that the ignition circuit is cutting out. I had this same issue on a car (malibu) and found it was an intermittent ignition switch connection. Replacing the ignition switch fixed it for good.
One thing that will really help you is to notice you dash lights when this happens. If the dash lights go out when the car stops, then this is it. If the dash lights (ignition) stay on, then you have another issue.

Look under the brake pedal, up near where it is connected. You'll have to get down in the floorboard. Push the pedal all the way down and see if the button contact is being pressed when you do. If it isn't, loosen it and move it up or down until it is. If it is being pressed in far enough for contact, it is most likely a faulty switch if you are certain the fuses are alright.

if you on a hill set the e brake then put in park. then when u wont to go again put foot on brake and release the e brake and put in gear try that and see i think this will help u

Torque converter clutch release circuit.

yes you can.. on your shift console there is a little square cover half a inch.get a thin screw driver and push it in. there is a button in there, step on the brake and shift the gear, with car on.  take it to the shop and they will put it in a scanner to see the problem...GOOD LUCK 

If you run a push button directly from the battery to the solenoid, the engine will crank when you push the button.

If the no start condition is because of the solenoid, this will not fix the issue.

If the no start condition is related to circuitry of the ignition system and/or fuel system, this may fix the issue, but may not, as well.

cord??dont you mean a cable ,this is the inhibitor so you cant put in gear without brake on .as button pushes in it pulls the cable up which in conjuction with brake releases the gearchange.it is possible to remove the lot just like the cars of yester year