hey people so my s4 has been having starting issues...now all the sudden i go to start it and it doesn't even make a clicking sound..

so since i bought the s4 in the cold weather we have here in saskatoon my s4 would take at least 10 attempts until it turns over and starts today in the morning it was being a pain. and while attempting to start the battery died out so i connected my other car with booster cables let it sit for 15 minutes and tried once to start and i smelt something burning in the engine bay. i ignored that was confused let the car sit for another 10 min when i went to go start it it doesn't even crank now. its like its dead i press the start button and hear a humming coming from the back i believe no clicking sounds no starter grinding noise pretty lost here...checked battery its running normal volts.
-the battery is new from audi