Sounds a little like my Noodles-except he does groom,just not very often
Could maybe need a little more active stimulation,as he maybe a little depressed-and try and encourage him to scratch for his claws as with him not going out etc his claws maybe uncomfortable for him,is it possible for you to take him for short walks on a leash/harness-this will make him feel a bit better about himself and he may then bother about grooming-but around this time of yr as Wendy said they do malt loads or at least my Noodles does
Also again diet will help his coat,maybe use a soft brush like a baby brush-and now and then just gently go over his coat and slowly work your way around to his hind legs/bum area-get him used to it and then take things from there