On the ink cartridges is an electrical strip which sits against the reading strip within the printer. 3rd party cartridges do not use the exact same strip as genuine Dell cartridges, which runs the potential of shorting out the 3rd party ink cartridges electrical strip, or worse yet the reading strip within the printer.
For the most part, printers will run without issue using a 3rd party cartridge, but overtime the risk of shorting out either the electrical strip on the cartridge or within the printer becomes greater.
In your case here, the strip on either the cartridge or within the machine has shorted and is no good. Test using any other cartridges you have and see if the printer will read them OK.
If other cartridges do work, then you just need to replace the new cartridges that the printer is not detecting as the electrical strip is shot.
If no other cartridges are working, then the electrical strip within the printer is shot. You can send the printer in for repairs, which may cost more than the machine is worth, but it may still be worth a try to see what the quote is.