Hi, Welcome to JustAnswer.com, I am glad you are here! My name is Eric & I will endeavor to answer your question.
The absolute first thing to do is for me to ask you to please tell me the manufacture and EXACT model number of your door opener. It is impossible to offer precision troubleshooting without my first knowing that.
I am now going to break down your original statement and offer some thoughts and ask some questions of my own. What you wrote will be in Italics, My thoughts will be in bold. Some of what I will say, you will undoubtedly already know, please be patient as I am only reiterating.
You stated "My garage door will not close unless I hold the button down.
I ask, will it open with a momentary touch of the button and as well, with the remotes? As others have said, your statement indicates that there is indeed a failure SOMEWHERE in the safety sensor circuit. This could be with the sensors themselves however, taking into consideration ALL you wrote this would not be the first place I would look. It could be in the wiring and it could also be an issue with your logic board which in my experience is not as uncommon as one might expect.
You wrote: "When the door is up, the sensor lights are off. After I hold the button down to close it, the sensor lights come back on".
I have read that with the door open you have removed the safety sensors and have held them at close proximity to each other and they still did not light.
If you have NOT already done so, please humor me and do this again this time however, with a NEW SHORT piece of wire connected directly between the safety sensor circuit on the door opener control head (ie: The Motor) and your safety sensors held in your hands standing close to the motor. If the sensors light this time, replace the old wiring between the sensors nd the motor unit. This should solve your problem.
If they DO NOT light when re-tested with a new short wire please tell me...
A. "When you press and hold the button to close the door when the safety sensor lights re NOT lit, how far does the door have to close before the lights go back on"?
B. If they go on before the door is all the way closed and you release the button, does the door stop closing?
C. If so, do the lights stay on?
D, If the door does not stop closing and you then tap the button once, does the door then stop closing?
E. If you tap the button once will the door start to reopen and do the lights go off?
F. If you repeat step A nd get to step B but WAIT until the door has traveled 6 + or - inches beyond where the lights come back on and tap the button, ANd the door stops and then you tap the button again let the door start up nd tap it quickly again to get the door to stop again but BELOW the point where the lights were coming on, do they remain on and if so, at this point can you tap the button once again and get the door to finish closing?
If the answer to A was that the lights do not go ON again until the door is ALL THE WAY closed.
1. When the door is closed and the lights are on, if you put an object between the sensors do they go off? Or, do they blink? Or, do they remain solid?
2. When do they go off again after you press the button and the door starts to open again?
Please keep in mind that just because a set of sensors might be aligned when the door is closed, that does not mean they ALWAYS stay aligned when the door is opened. This is because garage door tracks can flex just enough between the door being open and closed to allow the sensors to become misaligned IF they are actually only just barely in alignment to start.
Tell me the answers to all of these questions and as well, the make and model number of your opener and I will attempt to offer you a rational diagnosis.