There are few things, which can cause this problem. One, if the waste ink absorber is full or if the cartridge nozzles are defective or three if the logic board is defective. First try the steps from the video in the link below to reset the printer and let me know the result. If it fails then, I will give you the other solution.
The printer shown in the video may be different from your printer model, but the steps will be same.
Do you use genuine Brother cartridges ?
That can damage the printhead also. Please follow the steps below to clean the printhead and let me know.
Boil some water
Turn on the hot water until luke warmPut about 1/2 inches of water in a cupPut the print head portion (where the ink comes out) in for about a minuteDry off the cartridge using a soft tissue.Re-insert the cartridge into the printer.Run the normal cleaning software routine a few times
You have to use the normal cleaning method after cleaning the printheads manually.
Sorry, I misunderstood your question last time, you will need some luke warm water to clean the printhead nozzles, did you read all the steps, before replying me, because I have explained, what you have to do to clean the printhead manually.