We have a Genie H6000-07/M garage door. When we push the button on the wall to close the door, it goes down a little more than half way and stops. When you push the button again the door goes up.

Dear Erik,
Although I do not sell or service garage door openers as a profession, I will be glad to tell you you only need to adjust the door, and is should be fine.
There are adjustments on the motor, to tell when the door is the right distance up and the right distance down, and the chain must be adjusted correctly, and the rollers need lubricating oil, and the slotted tracks need grease.
With all these done, you will be good to go.
Most doors need this service every 3 - 4 years, with normal use.
I cannot tell you specifically how to do this, because each door is different, but you might get really good pictured help on "youtube".
God bless your efforts.

are the wires connected to the motor correct
for the limit switch there should be one wire ( normally black or neutral going to the center connection and the other wire ( red or active wires going to either of the other two terminals
that set up means that power is available to the limit switches and the return is the neutral wire
it works like this
on the up direction power is delivered to the motor by the controller box through a closed limit switch
when the up limit is circuit is broken the motor stops
the down button reverses the polarity of the motor in the controller box and so the motor runs in reverse through the the lower limit switch until that circuit is broken In the down action the upper limit switch circuit is completer but the control box has no power to it until the lower switch circuit is brokenis broken
the motor is dc voltage and to getting it to go up or down is done by the control box changing polarity for the motor power according to the button position pressed on the remote

On the back of the garage door opener there will be a button that you will push it will start flashing right then you will push the garage door opener button and do the same freaking packed push the button wait for the blinking light enter your code and pushed enter

So it seems the Main garage door unit on the ceiling is ok. The problem is with hand held unit. Usually the circuitry is ok. Try changing the battery. It has helped me. Also make sure the sensor on ceiling unit is not blocked ad is free of cobwebs.

Your photoeye safety sensors are not aligned or have a problem. If you hold the wall control the entire time the door is closing, it should work. Check to make sure you sensors at the bottom of the track are aligned

If the motor is jumping in the closed position then something is likely causing a safety stop. The two reasons most commonly are that something is blocking the sensor or the torque is too high. As the door will open Torque is not the probable cause. It is likely something in the protective door block circuit preventing it from going closed. If you press and hold the close button will the door close momentarily? If so then there is definitely something telling it that it is not safe for it to close. If neither of those Solutions work then you probably have a circuit failure which was the cause of the fuse failure in which case the solution is to replace the genie.

You need a general inspection of all related parts. Make sure none of the track mounting bolts have loosened leaving a misalignment of track segments. CAREFULLY with power off use fingers. turn EACH roller. Something as simple as a bad roller bearing can cause this, even a flat spot on a worn roller. Rollers can be bought at a home supply store. These are 2 most causes.

Sounds like a skinned wire on your front or rear limit switches is touching metal. Go over your low voltage wiring and test again.

Check to see if the Vacation switch is locked on your wall console. It is a switch on the top of the black wall button. If that is not the problem it sounds like you need to program your remotes. Drop down the plastic cover towards the back of the unit There is a learn button push that and a red LED will come start flashing press and hold the button on your remote until the LED stops flashing (solid red) press the button on your remote again and the light will go off. This will program a remote
Here is a copy of your manual
www.geniecompany.com/docs/GENIE%20EXCELERATOR-ENG.pdf

Anytime a door opens and/or closes randomly or doesn’t work consistently I look for a smashed wire between the motor unit and the wall button.

If the wire is smashed the insulation becomes so thin that power will leak thru the insulation and activate the door or interfere with the remote signal.

Loosen the staples with a small screwdriver and slide the wire about ½ inch to move any areas of thin insulation away from the staples.

The second thing would be a bad wall button or a remote with a sticking button.
Or a remote in someone’s purse that gets the button pushed by other stuff in the purse.

The test is to disconnect the push button wires at the power unit. If the self operation / interference stops you have located the problem. If you reconnect the wires and disconnect the wire at the wall button this will tell you if the problem is the wire or the button.

HOPE THIS HELPS