You don't take the cartridges out, if they have activated carbon you cut a small slice and shake out the carbon , you need them in there because that's what has your beneficial bacteria on it to keep your paramiters in check, they are dried out now which killed the beneficial bacteria, don't be surprised if your tank goes through a mini cycle, if you have the extra money I would get a good filter like an aqua clear hob that way you don't have to mess with cartridges.
So if you do here's how you will do it you will keep the old filter running in the tank, as well as the new one until the aquaclear has built up beneficial bacteria in the media (ceramic rocks) the aqua clear hob's have 3 stages, sponge, carbon, media (ceramic spheres), you never have to buy cartridges or anything unless you want to keep running carbon but carbon is not really a must have, so if you do have carbon in the aquaclear and you have to dose meds you just remove the pouch of carbon put it in a zip lock bag, leave everything else in it and then treat the tank that way you don't have to worry about killing your beneficial bacteria because the ceramics never get taken out
The only thing you do with the filter like once every month, month and a half is when doing your pwc clean the sponge in fish water you've siphoned from the tank and lightly swish the ceramics in the mesh bag it comes with to get the big debris off, never do this in clean water always use water you've siphoned out of the fish tank.
Also you never clean those cartridges in clean water either only fish water