From the symptoms you are getting, its quite evident that the print heads are worned out with usage or have clogged totally.
If you already tried cleaning the print head / cartridge then there are only two possiblities :
1. The print heads are worned out with usage.
2. The cartridge you bought is faulty (less probable)
If the printer is in warranty then you should get it repaired by Lexmark for free. If not, you will have to send it to Lexmark for print head replacement.
To be very honest, these print heads are made of poor quality so that you need to replace them and Lexmark can make money. Thats why they sell cartridges at cheaper cost. Cheapest option is to buy new printer.
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