The adjustment program the manual refers to is for resetting the ink counter once it reaches it's limit and making adjustments to the print quality. You can perform more intensive head cleans with the adjustment prog also.
Personally I would never insult my 1800 with anything but genuine Epson ink or a very good rival. Cheap compatibles are cheap for a reason, and it's not all down to profiteering.
I service epson machines, and you tell EVERY machine that is run on cheap compatibles, even when the punter sends it...
There could be an air bubble in the tube that takes the yellow ink. Once left for a while the bubble will rise and allow printing. After a few pages the bubble will be drawn to the head and stop the ink. Try running a head clean or two to suck the bubble out.
If you can't make it work right...
Just because the ink lights are not on does not really mean the carts are full. If the machine has been stood a while, it could easily have dried up. You could try the intensive cleaning of the print head and put some new cart's in to see if the machine can be resurrected.
Sounds like your printer has hit the Ink Overflow Protection Counter limit. I suggest you contact http://www.TheServiceManualShop.com and get a Rescue Kit. If you don't find one in the listings, ask them to create one for you.