My convertible top on my 2003 Mustang won't go up when I press the button. It goes down fine, but I have to manually lift the top to the halfway point, then the car takes over from there. Any suggestions on what the problem could be?

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Check to see if the top motor is running when you press the top up switch. Car has to be in park with emergency brake engaged. If motor runs but top will not move or binds then one or both of the lift cylinders are bad. Usually there will be hydraulic fluid leaking from the cylinders if one or both will not hold pressure. Replace cylinders if bad. The top could probably be manually closed if the lift cylinder arms are detached from the top frame.
If motor does not run when the switch is pressed then check your fuses, the switch and the connector at the top motor to see if it is getting power.

most soft tops are operated with an electric wiper motor could be just a rust problem, check behind the seat or in the boot of the car, these are normally behind a panel, a little Q20 should sort it out

check fluid hear pump run

If the convertible top switch not working properly every-time.Then the switch and its electrical connections/wirings needs to be checked. The switch is typically located in the trunk, positioned right beside the covering of the left or right tail light. The switch should be set to automatic, not manual. If the switch is properly set, then other things are causing the problem. The other things blocking the top to move up and down is its hinges.If the hinges are bent or cracked or got loose then this can be the other reason. If the hinges are in good condition, then check the convertible top struts. These are the mechanisms that lift the convertible top. Lift struts deteriorate due to wear and tear and will need to be replaced if it's the source of the problem. Another very common reason for a not working convertible top is the worn out elastic straps. Furthermore, the convertible top's fuse could be blown out and as a result it's causing the convertible top to stop working. In newer latest models the convertible top is controlled by a single button conveniently located next to the handbrake. You press a button to release a center locking device - none of this moving the sun visors out of the way and releasing two latches on other sides of the car stuff! - then twist the device with its conveniently large handle. Then you press the button, and if you're lucky, it'll work the first time. If not, try it again! The temperature display goes from blue to yellow and shows a "convertible top opening" graphic, and the top opens up and neatly folds itself in back. You can release the button when it beeps again. Putting it back on again is the same basic process, though you have to wait for the beep, then press the latch release, twist it, pull down, then re-twist the latch again. Thanks. you can rate this solution and show your appreciation.

Manual roof procedure
The procedure in the manual is just for closing the top.
A) Turn key to OFF for several seconds to bleed off hyd pressure.
B) Turn key to MAR (full electrical, but before start)
C) Remove cap on bulkhead behind the right-hand seat and use flat head screw driver to unfasten the hyd unit valve in order to relieve the oil pressure in the circuit.
D) Remove the cap on the bulkhead behind the left-hand seat and using screwdriver or allen wrench press until the top covering (panel behind roll bars that covers the convertible top well) until the panel's locks are released - you may have to tap the wrench to release the locks.
E) Lift the top covering manually and keep it open while extracting the top from its well.
F) Remove top from well until the front part is near the windshield frame.
G) Lift the rear part of top (rear window) upwards and lower the top covering until the hooks are resting on their respective locks.
H) While still keeping rear part of convertible top lifted upward press Button 1 to attach the top covering locks.
Button 1 is the forward one
Button 2 is the rear one.
I) Make sure locks are fastened. if not - try pushbutton 1 again. If necessary repeat D and H
J) Rest rear part of convertible top on top of covering.
K) At front of convertible top, open (deploy) the top's hooks by using allen wrench to turn the pin mechanism. (located in center of front headliner)
L) Press top unto windshield frame and use wrench to lock the hooks.
M) Press the rear of convertible top, so hooks on rear top insert into respective slots and press Button 2 to secure.
N) Keep Button 2 pressed until hooks properly fasten.

If the top is still tightly latched at the front, you can just start at step "G":
While holding the back of the top in the air, and the "top cover" resting down on its "hooks", press button 1 until it seats well.
Then lower the back of the top down to mate its "hooks" and press it down while holding button 2 until the top seats well.

You are probably low on fluid.
Behind the rear seat is the motor/pump/reservoir.
With the top down, fill the reservoir with ATF.
Cycle the system a few times.
Repeat till the reservoir will accept no mor fluid.
Chedk the lines and cylinders for leaks. The fluid must be going someplace.
You can change it to a manual top by removing the bolt at the top of the cylinders and lowering the both shafts down into the cylinders.

There is a fuse No.20 (15amp) in the under dash fuse panel and a 25amp circuit breaker in the under hood fuse panel that controls the top.

Sounds like the switch is bad. Also check the relays. You might have one for up and one for down.

the motor is burn or disconnect