I had one that I knew was full but it wouldn’t work. I bought a widget that resets the ink levels in the cartridge – for use by people who refil their own – and it worked a treat. Cost only a few quid less than a new cartridge, but at least I wasn’t throwing good ink away.
EDIT: some cartridges for super cheap printers are actually the print head and cartridge combined together. Therefore they contain lots of gubbins that could quite easily go wrong I suppose.