Thank you for trying, that 5100 is specific to a carriage fault,
so repeat the above steps but focusing on that encoder strip and the movement of the carriage.
If that still doesn't help, it would unfortunately confirm an internal hardware failure. This is a 2013 model, so it is at the end of the maximum 3 year service life that Canon designed it for.
This is something that would require repairs to correct; at that point it is time for a new printer. While it can be fixed, it is not practical to do so. You'd be in the $150 range to have the internal power supply replaced, and a logic board would run you $200-250. For $80-100 you can replace the entire machine with a brand new model, with current technology and a fresh warranty, which makes more sense than buying new parts for an older printer.
If looking for a replacement, I’d recommend any of the Epson workforce series printers. They tend to be very reliable, are easy to set up and use, have good print quality, and reasonably priced ink. Example: http://amzn.to/29wF4OP or http://amzn.to/1NYUF1P
Note that these, like all consumer grade inkjet printers, are designed to be low cost and are essentially disposable after a few years, subsidized by the high cost of ink cartridges. If you wish to have a better quality and longer lasting printer, that comes with years worth of ink up front, consider the Epson ecotank models instead: http://amzn.to/1PpOj0C
Alternately, for a more business/commercial grade product that will be rated for a 5 year life, consider a laser printer. Lasers cost more up front also, but a toner cartridge can last for thousands of pages. A black only all in one laser is around $125: http://amzn.to/1JSHOlQ
while a color model is about twice that: http://amzn.to/1n4I7Q5
Best regards, ***** ***** for the news,