EPSON printers are categorically and without question CRAP.
£250 bloody quid I paid for mine and it's simply a damn licence to print money for f-ing EPSON. NEVER EVER EVER EVER AGAIN WILL I BUY AN EPSOM. EVER £16 for a cartiridge of which there are 8 of them and the printer absolutely gobbles them up - the 'replace cartridge' light is always on.
Anyway, rant over - your print heads are clogged, it has nothing to do with the new-ness of the cartridges. They are nigh-on impossible to clean - don't bother with the auto head cleaning routing as this will empty your very expenisve cartridges of about 5% of the total ink. I am an engineer and tried to take my printer apart just so as I could access the heads and clean them with some spirits - I gave up & if you ask me the thing has been designed in such a manner as to make it nigh-impossible to access the heads.
In desperation, my wife bought some an actual head cleaning cartridge off the internet - but I was so wound up with the poxy thing (and that she had spent even more money on the bloody thing) that I never got round to actually trying it.
What I would do if I were you was take it back to the shop & complain - they are not fit for purpose, get your money back and get a colour laser printer.
Honestly, the best of luck with this, but you'll need all the luck you can get if you're gunna get it fixed by Monday.
Andy
PS
EVER