kitty cats are a good thing!!! i bet your cat really really liked that you played with him/her!! i have two dogs that i love to talk to and watch and interact with. sometimes they are the only 'people' i talk to for days!! best part they don't seem to care that i'm a little nutty...they like me anyway.
sleep is not a bad thing. sometimes it's what helps us get through the day. and even staring off into space isn't so bad if you can at least try to think of something...don't want you to go all catatonic on us!
personally i think you are doing awesome just playing with the cat, staring off into space, sleeping AND writing here! when we're depressed that IS a lot!
be kind to yourself. we all know the depression will ebb and flo... right now you are in a really poopie place. ride it out. and give your cat some kisses!!