Printer covers page in cyan, magenta and yellow. Image attached.

This points to a drum or grounding issue. The first thing you want to check (this is unique to Brother and some older laser designs that lack the PCR roller design) is to take all four toners out and "clean" the charge rollers; there's a plastic tab on the drum when you remove the toners on the right (blue tab) that is used to clean the corona wires; even a broken wire can cause this defect (while it's not common, it happens; this is why the PCR design is the preferred method now -- if it feels too loose or jams, the corona wire may be broken). Move it back and forth 3-4 times, and see if it still occurs. If the issue remains, you'll want to check the printer's ground points and see if any in the drum may have toner causing poor contact and if the toner has a similar issue. I have seen similar problems occur on every brand, especially if you have left packing material like separators on the new toner installed, which will produce a similar issue. Double-check all four toners for packing materials like separator tabs.

So we can better see what yours is kaid out like, take some pictures with the drum and toners removed so we can identify the points better. The Brother DCP series generally has it on the side of the frame, not in the drum. However, the drum will also have a ground point. It will probably be on the side once you remove all four drums, but not under the ITB.

I use Lexmark laser printers, so the ground will not be in the same place as that of these Brother DCP color lasers. That said, it's usually on the left or right side of the frame with direct path color lasers like the Brother models.

If the grounds look good (and no residual toner on them—yes, this can/will cause issues like this), replace the imaging drum and see if the problem remains. A faulty drum unit can cause this if it isn't due to a poor ground point or a major machine fault, even if only one part of the drum failed. If the issue remains with new drums, you have a major ground fault that you will need to chase down.

The drums are not piecemeal on this DCP - these use a single component drum.