Could if lucky just need a head clean/maintenance ran on it have you tried all those? Though from the amount of splurged ink it looks like it could be more serious.
Another thing you could try if it is possible with your printer is removed the carts, lay a thin layer of kitchen paper/towel on its possition where the print head travels and if its possible move the head manually over it back and forth a few times CAREFULLY to see if that gets rid of it.
If that does not help then its either a fault with the cartridge or the print head is knackered.
There will be no solution unless you want to replace the print head and in many cases that is going to be cost prohibitive or skill prohibitive.... New printer time
I personally wouldn't mess about if i were going to spend that amount on parts, you may spend 100$ plus on a part like that and it still not work. Id buy the head unit complete rather than just the top half of it and only if it worked out significantly cheaper than a new printer of similar spec, which i doubt will be the case in your situation.
Entirely up to you though... Maybe hunt fleabay or similar for a printer the same model of yours but with a different problem (such as paper feeding for example) and rip the parts from that printer what you need, may be a cheaper way to go if you are insistant on fixing it.