You don't need the service program for any of this. You do need to either enter service mode to uncap the head, or unplug the printer while it's in the middle of moving the head in order to unlock it from the cap unless you open the entire right side up and turn the gears manually. iirc the service mode is hold OK, right, and down while powering on-- I literally had to recall this by putting my hand in the cramped position I use to press these buttons at the same time then thinking about which buttons those actually would be. The service program is really only useful if you replace the head and you need to write to the motherboard the new code which contains the ideal voltages for the new head. The name of that value is escaping me at the moment, but it's not necessary yet.
You COULD replace the whole assembly-- basically it consists of a flat backplate with very thin tubes that connect from the ink tubes themselves (see attached photos). This distributes the ink to the 5 dampers, each of which handles two ink channels. In the case of the black ink on this model there is another set of "sub dampers" and a motor which changes whether matte or photo black ink ultimately flows into the damper for that channel. If you're paying attention you'd realize that there are actually 10 channels here, and only 8 inks being used at any given time, and yes, that's because this printer is identical to the 9900 just with two empty slots where the orange and green could go. So you actually have two unused channels in your head that can't be used here. Epson easily could have had both matte and photo black loaded simultaneously in the 9890 by utilizing one of these extra channels, but they didn't want to have two different SKUs for the damper/ink selector assembly, so you still have to waste time and ink swapping between the two even though you have an empty damper and two extra channels sitting right there.
Anyway, the dampers connect to that backplate by snapping into a clear plastic housing-- they're a little tricky to get out, but once you've done it a couple of times it's not so bad, and then you can rinse out and clean each damper individually (or replace them) instead of replacing the entire assembly.
if you're going to start messing around with this BE DAMN SURE that you eject at least one cartridge before turning the printer off and starting to unscrew things, otherwise the system will stay pressurized and you'll have ink spraying out everywhere (instead of dribbling out, which will happen regardless). It's a messy process, and there are lots of opportunities for causing bigger problems-- the flat flex cables leading to the head are particularly sensitive, and they can tear easily, but I find that it's even easier to get a tiny bit of ink into the slots where they connect to the head, which causes a short between pins, and usually will at least blow a microscoping fuse on the motherboard when you next power it on if it doesn't take out the whole board itself.
Also I know I'm skipping some steps that are just muscle memory at this point, but the printer should be unplugged, and after unplugging it you should try to turn it ON again, which will help drain the caps on the motherboard so there isn't any electricity still stored in them. Either way it would be wise to leave the printer unplugged and alone for 30 mins or so before starting to do anything that involves plugging or unplugging wires just to be safe.
It's funny to me that they have protections on this board against shorts, but epson only ever instructs techs to replace the whole thing (at a cost of ~$2000). A few times I've blown these fuses, and once I found out my error I either replaced them or just bridged the connection with a bodge wire with full realization that if I ever got to that point again I'd end up frying the board. That usually has only been at a point at which the printer was about to be thrown in the trash anyway (11880 converted to dye sub I think was the one I had to do that to-- god what a nightmare that thing was).
Anyway all of this is a pretty major digression-- you could end up cleaning all that out and not get anywhere in terms of fixing your actual issue. I keep talking about reverse suction on the head, and that's actually what I would try first in this case--
Once you get all the covers and things off of the head carriage there are only 3 screws that actually attach the whole damper assembly to the printhead itself. One is in one of those rectangular holes in the middle, and two are on the sides-- I believe these screws are usually black to differentiate them from the rest of the ones that hold the assembly itself together. Once you remove these screws you can gently rock the whole big plastic assembly back and forth and pull it straight off of the head-- in the case of the 9890 since you're at an angle I'd put some paper towels down underneath this area to catch any ink dripping out. You also need a pretty long philips to be able to reach these screws, especially if you haven't gone through the whole procedure of removing the top cover (which absolutely sucks). The added bonus to taking off the whole assembly is that the dampers offer some protection from the ink just flowing out all over the place, since they're literally there to regulate that pressure. They allow ink through via suction, not via pushing it, so it's actually the action of the printing and firing nozzles itself that keeps the ink flowing through them-- otherwise you'd need to press on the sides of them to allow the ink to pass through.
If you've gotten this far, and things are not totally destroyed yet, you can gently pull the 4 flex cables out of their slots on the head, and then there are 4 #1 philips screws that hold the head in the carriage. After that point you can remove the head. The picture (the one that's actually mine, not the obviously ripped from the internet one) is of the top of the ink selector assy of a 4900-- this one is considerably easier to access because of the orientation of the machine and less stuff in the way, but it's identical to the 9890/9900 in every other way.
