Oh dear, what a shame. I have owned 3 Epson printers and the only Epson cartridges I have ever used are the one supplied with the printer! My photo 925 and my wife's C66 continue to work perfectly. I have never had an Epson printer problem that can be blamed on "equivalent" cartridges. Although, I can't be certain, but this problem can happen if you leave the printer switched on for ages without using it. Better to power it off when (I think) some form of cap is fitted over the jets to prevent them drying out. The only suggestions that I can make are to try fitting a cleaning cartridge and leaving it in place for ages, running plenty of cleaning cycles, but then if the jets are blocked, you won't be able to suck the fluid through. Thus, in the extreme emergency that you are now in and as all else has failed, malt vinegar may be your answer. If you can manage to remove the jets themselves then soak 'em in the chip shop fluid for, maybe, days. If you can't then your only hope is to deposit some in the top of the jets which you can get to once the cartridges have been removed Then put the cartridges back to stop any chance of the system drying out. Again patience will be necessary.
I must stress that this is what I would try if all else has failed. I have never had to do it myself on an Epson printer, but it is the unofficial cure to such problems with HP ones which has worked for me in the past.
With regard to equivalent cartridge suppliers, as PPRuNe curently has an advertiser marketing such materials, it would be wrong for me to post a link to mine - but I have in the past. I'll say no more!
P.P.