This is an update for anyone that might be following this thread or for in the future.
TL;DR -
So, I believe all of this was caused by a possible corrupt HP 951XL Yellow cartridge. My next step is to troubleshoot another HP 951XL Yellow cartridge and test if the problem exists with that particular color, that particular yield capacity, or that particular cartridge. Another possible next step would be to purchase a new HP 951 Yellow (standard-yield cartridge), but I am not going to start buying random cartridges just to troubleshoot what I believe is a single corrupt XL cartridge. I am currently waiting on the delivery of a new HP 951XL Yellow cartridge, and in the meantime, I have initiated the process to return all of the new cartridges, but I will wait for that return until I can troubleshoot with the new HP 951XL Yellow cartridge.
TL;DR -
I spent at least an hour trying to find what might be causing a paper jam (that in turn might be causing the error messages stating the carriage is not able to move). I was, however, able to manually move the carriage back and forth with no problem. I knew all along (at least I felt quite sure) there was no "paper jam", but that "something" was causing this carriage lockdown. These error messages did not allow me to navigate to the home screen on the printer display panel, so I was not able to troubleshoot in that direction. I began to think about a possible printer online update gone wrong, so I uninstalled/reinstalled the software. The errors still existed.
Once I decided to move away from this non-existent paper jam, I began to troubleshoot whatever moving parts I could touch. I removed the print head as I recently read about other people having similar issues, but those who replaced the print head either did not report back, or the new print head did not solve their issue. I was certainly not going to spend $120 to replace something that I was not sure was the problem, much less at a price that was half of the cost of the printer when it was new! Reseating the print head did not change anything. During all this time, I had performed several printer resets, but because I was not able to clear these error messages, I could not navigate for a hard reset.
The next thing I thought about was to check the printer cartridges. I might have to back up a little with the chain of events because my original post was more about printer warranties and less about my particular issue that lead me to complain. The day before this thread, I printed a small colored graphic, and within 3-5 minutes after that print, my printer display panel began to erratically blink random lights, then I heard some loud clicking noises, then the sounds from the printer that you hear when it is turned on, and then the error messages appeared ("Carriage Jam" and "Cartridge Problem"). In hindsight, if the error messages would have left out "Carriage Jam" or simply reversed the order of the error messages, my first thought would have been to check the cartridges, but no, I had to waste hours looking for a "jam" of some kind that did not exist!
I bought some new cartridges about a month ago, and again in hindsight, I wish I would have started troubleshooting the cartridges. I have always used HP 950XL Black (this is the high-yield cartridge), and HP 951 Cyan, Magenta, and Yellow (these are the standard-yield cartridges). This time, however, I decided to try HP 951XL Cyan. Magenta, and Yellow (the high-yield cartridges). Within the month, I only printed black/white documents, so I do not believe any color was used. I began to switch out the HP 951XL Cyan with the previous (depleted) HP 951 Cyan; the error messages remained; I switched them back. I switched out the HP 951XL Magenta with the previous (depleted) HP 951 Magenta; the error messages remained; I switched them back.
At this point I stopped and removed ALL of the cartridges, and while the printer was still turned on, I performed a power reset (unplugged the power cord from the back of the printer and then the wall outlet, waited a couple of minutes, plugged the power cord back into the wall outlet and then the back of the printer - all in this exact order). When the printer resumed power, the error messages disappeared! I took advantage of this and performed a hard reset. When the printer powered off, I reinstalled the new cartridges, but as soon as the printer received power, the error messages appeared.
Over the next 15 minutes, I tested the above steps in random order. I believe I found the problem! I realized that the moment I installed the HP 951XL YELLOW cartridge, the carriage immediately locked down and the error messages appeared. I had to remove all of the cartridges and perform a power reset to remove the error messages.
So, I believe all of this was caused by a possible corrupt HP 951XL Yellow cartridge. My next step is to troubleshoot another HP 951XL Yellow cartridge and test if the problem exists with that particular color, that particular yield capacity, or that particular cartridge. Another possible next step would be to purchase a new HP 951 Yellow (standard-yield cartridge), but I am not going to start buying random cartridges just to troubleshoot what I believe is a single corrupt XL cartridge. I am currently waiting on the delivery of a new HP 951XL Yellow cartridge, and in the meantime, I have initiated the process to return all of the new cartridges, but I will wait for that return until I can troubleshoot with the new HP 951XL Yellow cartridge.