If yours is anything like my HP colour printer there's a belt which moves the paper across the different colour processes. Either that or the belt drives something else in the computer which moves.
Unfortunately at the price level of this printer you can't just leave this till the part breaks finally and then buy a new printer. You have to decide whether you can work out which part, remove and obtain replacement and fit it. Or whether the cost of a repair shop is justified. My first step would be to contact Brother and get them to clarify the error message and how easy replacement part is to fit .