Why will my Brother MFC 290 C printer not print black ink anymore?? I replaced the cartridge and it will not print anymore!

Unfortunatly this is a known issue with these machines and often times the printhead needs to be replaced which need to be done by a service technician.
If it's still under warranty you can contact brother who will direct you to a local warranty shop for service, if it's out of warranty all you can do is try running the Power Purge operation a few times to see if it clears up.
If the Power Purge doesn't help and it's out of warranty you'll need to replace the printer as the cost of fixing it will be more than the cost of a new printer.

Here's my solution on how to run the cleaning mode from another post here on FixYa:

You'll have to run the cleaning mode a few times,
to do so you'll have to get into Maintenance Mode.

To do this:
Press MENU then * then 2 then 8 then 6 then 4
This takes some practice and you have to press them all within a few seconds.
If the machine doesn't say MAINTENANCE when you do it press STOP/EXIT and try again.

When in Maintenance Mode:
Press 7 then 6, then press 3, then press BLACK START
It will say Cleaning - this will take some time when it's done it will go back to MAINTENANCE

After it's completed try 0 then 9, this will print out a small Print Quality test page
it should have several rows of each color (Cyan, Magenta, Yellow and Black)
if they still don't look right then run the cleaning mode again and then print another quality page.

Continue to do this until the quality is back to normal,
when you're done to exit maintenance mode press 9 then 9 to return to normal operation.

note: this cleaning mode uses up a fair amount of ink, use sparingly

note: maintenance mode is for brother technicians and has some codes that can damage your machine, only use the codes I've explained in this solution