For Ink cartridges with the print heads on them you can take a container
lid and fill it with real warm water and set the cartridges head in the
warm water for a while , take it out and dry it off with paper towels .
This can be a mess but sometimes it does work .

I like HP printers and have a newer one that uses those real small
cartridges 56 or something . It always works and wasnt very expensive .