Apartment help!

So we signed a new lease last week and upon looking through all the cupboards and stuff, we found that it was pretty disgusting. Nothing had been cleaned at all, there were bottle caps on our balcony, sticky stuff, flour, spices, hair, you name it in the cupboards and drawers. There was literally pee on the toilet, mounds of dust in the air filter and corners of the room, flies dead in the light fixture. He said the carpets had been cleaned but when we recleaned them, the water was disgusting. The next day our AC stopped working, we still had holes in our carpet (still has not been fixed), dishwasher overflowed because it was clogged, and faucet was leaking because the handles were so old that they didn’t work properly anymore. He fixed our AC and dishwasher but we are still livid. We told him we do not want to pay for last weeks rent (the rest of the month is fair to pay in our opinion) since our apartment wasn’t truly in livable condition. He keeps ignoring our request. Are we wrong to feel this way? Would you fight it? I didn’t take pics of everything but I did get these. Vacuum was clean previous to vacuuming