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2004 Mini Cooper S Repair Help

So as the title suggests I have a 2004 Mini Cooper S and I’m looking for some advise as to what I should do about fixing the car.
Recently the belt came off the car with no warning , just happen to be driving and then I noticed all the gauges going funny on me and sure enough when I looked under the hood the belt was gone. I’m thinking it is the tensioner pulley as this is the third time this has happened in less than a twelve month period and that I’ll be able to get fixed later on this week. The reason for the post is because just a little bit, say a month or two, before the belt came off I started to have an issue when i would go to accelerate the car from a dead stop. If i was too to quick to accelerate, then the car would suddenly lose power and the traction control light would start to flash and the only thing I could do was to take my foot off the gas, and after a couple of seconds, the light would go off and then i could accelerate like normal. What i was wondering is if this could be related to the problems with the belt or if this could be some bigger problem , someone had suggested that it might have something to do with the torque converter and that to fix it would cost more than I could afford to spend.