Well done, Gemini. Sounds as if you're going to do this wretched race or expire in the process.
Don't train seven days a week! You do need to start running, though, and if you have gym membership then grab a passing personal trainer and enlist their support. Get on the treadmill, set the incline to 1% and ease up to brisk walking pace, keep that going for a couple of minutes then step up the pace so that it's ONLY JUST too fast to walk, and jog at that speed. It might not be much more than 4mph, but that's you running. Do that until you get bored or a bit breathless, ease down, cool off by walking then do the same again. The whole session should take no more than 15-20 minutes.
Be sure to get good running shoes. Another worthwhile exercise is to go out and walk 10K just to see what the distance feels like. Measure the time - that's your 10K baseline on which you will, with training, improve mightily over 5 weeks. It will also prove to you that you will finish that race even if you walk it all.
Run, walk or do a mixture on three days a week, and do a different form of exercise on at least one other day. If you'd like to use another piece of CV equipment to warm up, that's fine.
Keep us posted about your progress.
Cheers, V-rap.