You have put the exasperation of a persistent paper jam indication in a nutshell, admirably.
However, there are solutions to the problem that sometimes do not involve junking the printer or replacing it or both.
The fact that the paper does not even feed out of the paper tray, is indicated paradoxically as a 'paper jam' in some printers. Others more expressively and more accurately say a paper jam is a 'Misfeed' - more applicable to this sort of 'pseudo-jam' (as it were.)
So the paper isn't feeding from the tray.
If the problem might possibly be owing to aging roller surfaces (for paper is fed into faxes and printers with rubber or plastic cylindrical rollers, that propel the sheet into or through the machine)... then you might need to clean the rollers in the problem area where feeding is not happening.
Remove all paper from the machine, unplug it, and open it so as to have access to the rollers in the problem area where feeding is not being done properly.
Take a clean high-quality lint-free rag cloth, moisten it with rubbing alcohol, and rub the rollers firmly all over their paper-contacting surfaces, three times over.
(If the rollers are hard to reach, there is another way to clean them... let me know if that is the case, and I will detail how to do the cleaning.)
Allow 5+ minutes for drying-off, then reload the paper, close up the machine where you opened it up, and then try again.
- Let me know how that goes. I hope it works out some, at least - making the paper feed in a bit if not all the way, would be a positive indication that the paper feeding rollers near the paper tray are indeed the problem and that more cleaning, and/or roller replacement in that region, would be needed to fully cure the problem.
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