yes true it won't strengthen your relationship. Do you have random conversations? Just bring up random things and you talk, i'm sure he will eventually even if he's not that interested. Do you see each other every day? if so then it'll have to be random things, if not then tell eachother in detail about stuff you've done. Ermm... tried non sexual intimacy, like massage each other. Go for walks round your neighbourhood, it might be a dump (i think that's how you put it) but i'm sure just walking n talking or just walking is still alright. Do you have any common intrests like music? can he play an instrument you cant? perhaps get him to teach you, or teach him if u do and he doesnt. Pick a hobby, absolutely anything, and do it together.
That's all i can think of for now :)