Don't give up on it. You have to remember that cactus stores up water in the body of the plant and does not need frequent watering. I trimmed my prickly pear back in March and just found one of the pieces in the corner of my greenhouse. It was still green. I trimmed off the dried area where I had pruned it off and now I have it sitting in some dirt. I expect new growth within the next few months. I have done this before :).
I would stop watering it and repot it in dry cactus soil. Do not water it after repotting for at LEAST two weeks. I'm definitely not an expert, but I have a large number of cacti. Watering once a week is way too often. Especially with it indoors where it is cool. It will need much less water in that case. You should go at least two to three weeks between watering. If you really can't control yourself, just dribble some water (like a tablespoon) on the plant once a week. And yes, MORE sunlight as mentioned before :).
Good luck!