I've got this on my 3800, again in the magenta head, and no amount of cleaning/checking/turn off or on cycles will do the trick.
I've also tried the magic bullet option, and used a variety of other surfactant cleaners that are basically the same (there are many similar products available including a variety of kitchen and bathroom cleaners).
The printer still makes a pretty good print, but the nozzle check will not go clean and occasionally I get banding.
Like the OP I've had this printer about 7 years. My attitude is that is good milage and maybe its time to wave goodbye at this point.
I called a printer dealer who does trade ins and he won't touch it, in his view the head is finally screwed beyond fixing. So if it has no value to him, I guess it has little value to other people too.
So my order is in for a p800, and the option to use rolls, a better inkset and a lot more convenience via the wifi interface.
I'll be interested to see if anyone will buy this on eBay, that itself should tell us whether a 7 year old printer with a permanently blocked head is of any value to anyone.