I'm not a lawyer or legal guru of any kind... just a been there, done that kinda person.
1) Since they are being unresponsive, do you have "proof" that you requested maintenance repairs? Did they sign any request you gave them or can you submit the request online (and if so, did you print yourself a copy of the request)? If you have none of these things, I would send my request to them via certified mail, return receipt requested. This will work in your favor should you need to take them to court later (i.e. if they refuse to deduct the repair money from your rent). Of course, you could do another letter, hand deliver it to them and ask if they would sign it... but the way things are going, that's not likely.
2) Does your lease say how long they have to complete needed repairs? If so, in your letter, state that they have _____ amount of time to make the repairs and that, if they don't, you'll have someone else do the repair work and deduct the cost of the repairs from next month's rent.
3) Take pictures of the leak, water damage (if any), etc. Pictures are quite valuable should you need to go to court.
You might consider speaking with a legal services rep in your area since he or she can read your entire lease and tell you exactly what to do and in what order to do it. There will most likely be a small fee for a consultation.
My best advice is to follow your lease and
document, document, document... have "proof" of request and of needed repairs.
If you finally get that @#$! thing turned off, keep it on A/C and turn on your oven to get toasty (open the oven door), if needed (yes... been there, done that too). At least you can warm up and still use the A/C when needed
