As EBarnacle says, the first step is to carefully get all the accumulated crud out of the insides of the machine.
You can occasionally get some improvement by "cleaning" the roller that holds the paper against the fuser using a rather simple expedient of printing a solid black strip on a sheet of paper, turning it over and running it back through the machine.
The pressure roller can pick up crud, and it runs against the actual fuser drum "between sheets," so it can contaminate the drum surface. Since the fuser drum is hot it can also pick up crud just from normal printing - which it may transfer to the roller. With the black-printed area against the roller, the fuser that actually "locks" (melts) the ink onto the paper will soften the "backside" enough to suck up (some of) the trash.
Some older HP laser printers ran a test print automatically each time you inserted a new toner cartridge, with an appropriate "black stripe" and instructions to turn it over and run another test print as a "cleaning cycle."
If you have Word, you could make a "cleaning sheet" by putting a box around a 10 or 12 line paragraph, and setting shading to black, then setting font color to white. (Be sure you have the whole paragraph selected, Chose Format - Borders and Shading. On the Borders tab, Click on a Box, then click the Shading tab and select Black. Next chose Format - Font and select color White. It should give you a solid black area with white letters.
Print it, turn the sheet over and print it again - if you don't have printing on both sides, turn it over different and print again.
There are no guarantees on this, and if it doesn't work the first time or so, you'll need to look elsewhere. (About 2 passes of the same sheet usually fuses the ink so much it won't pick up anything anymore, and if one sheet doesn't do it, you've probably got a different problem.
If cleaning doesn't help, the most likely thing I can think of is a bent or broken "charge wire," or misplaced discharge brush.
(BTW - "replace toner cartridge" is a maintenance procedure? Is this a 'bin-charged' printer? I'll have to go look at Brother. I "burn up" a toner cartridge about every other month - and get all new parts in the critical places.)