I have a HP Deskjet F2480, that I got for free, and which I think is identical or nearly identical to your F2418. I have successfully refilled HP 300 black and tri-color cartridges a few times, but rarely successfully more than once. A cartridge that was empty but OK, was indicated as defective after a refill. I think that successfully refilling the black cartridge 3 times is well done
I powered up the Deskjet F2400 and it indicated 2 bad cartridges, but when changing the cartridges with others I could make the ink lights go out. The cartridges didn't print very well as they were very clogged, but this behaviour leads me to think that your printer might be OK with a new set of cartridges, but I cannot give any guarantee.
If the tri-color cartridge doesn't indicate defective, it might just be empty or dried out if it is more than two years old. You could try to refill it or dip the printhead in a few millimetres of window cleaner with ammonia in a shallow dish for a few minutes. Test if the cartridge will give off ink by pressing it against a piece of soft absorbent paper. You might be lucky and revive the cartridge.
These inexpensive printers are priced similarly here in Denmark. The price is about the same as a set of HP 300 XL cartridges, but a new printer comes with the much smaller standard cartridges. So if your printer is in good mechanical condition, as it ought to be if it has seen only little use, I suggest to buy a set of XL cartridges. Even if it is a bit of a gamble, you could also try to look for a set of remanufactured XL cartridges but don't pay much more half the the price of original HP cartridges.
If you decide to buy a new printer I would recommend a Canon
with individual ink tanks (cartridges), as these ink tanks are much more easily refillable than the black and tri-color cartridges used by both HP and Canon in the more inexpensive models. For the Canon ink tanks resetters are available so you can reset the ink tanks to full again after a refill. HP also has a series of printers with individual ink tanks, but no resetter is available.
These printers are more expensive and you will have to invest in refill inks, a resetter and other accessories to refill them. If you only print
very little the best economy might be to buy a set of XL cartridges for your printer or in worst case a new two cartridge printer, as you have to refill a set or two of individual ink tanks before your investment in inks, a resetter and other accessories is paid back. From then on you will save a considerable amount of money when refilling. You will be able to refill a cartridge for less than 10% of the cost of a new OEM cartridge.
What is the best thing to do? I don't know, you decide. It depends very much on how much you print.