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It sounds like a hardware fault rather than a software one. Are you using genuine Kodak cartridges or the generic brands?
The most likely cause will be a blocked print head, the inks work fine (I use generic myself), but if you dont use the ink regularly they dry on the print head very easily, and also leave residue over time which builds up - as the chemical in the ink are cheap.
You can buy printhead cleaners such as the one here, from experience its 50:50, personally I would buy a new print head such as the one here.
To confirm its the print head, does the page 'print' just with no ink of the page?
Have you tried printing a black only page, such as some test on a word document. If the page goes through the printer do you see the print head go back and forth as if it was going to print, but just no ink shown on the page?
Excellent this proves its a print head issue.
The automated\inbuilt print head cleaner is not designed to clear a blocked print head, but to improve picture sharpness and quality. For example where you start to get bleeding on the page etc.
There is special chemicals which you manually syringe into the print head which breaks down the blockage, this is what the kit referenced above is for.
I personally would suggest you buy a new print head however, since alot of the time (n my experience) the blockage doesnt clear.
Instructions for replacing the print head can be found here.
A new print head is around £45 the head cleaner is around £12.
If your happy with the printer and have cartridges for your current one I would replace the print head, but I agree with you its starting to get towards half the cost of a new printer.
Unless you have any follow up questions, I would appreciate if you can rate the service received so I may close the case.
If the fault isnt cleared by a new print head you can respond back and happy to arrange a refund as the issue wasnt resolved.
Appreciate if you can rate the service using the star rating, we have a 30 day money back guarantee should you still have issues, but I am confident this will resolve your problem.