Audi V8 Start problem

Hello, I happened to have a V8 two weeks ago. The car is 2 hand and top maintained, so I couldn't stand again. The Audi TOP was running during the purchase and also for the next 3 days !! I am positively surprised about the car, otherwise drive 7 BMW (hope, I will not be stoned here therefore !!).
So, here's my "beginner question": Got the car now about. One week not moved, now the car started coughing at the start attempt and one had the feeling that it did not run on all cylinders, also went out immediately again. I thought about charging the battery and checking the spark plugs + cables (marten bite). But these were fine. So I installed the charged battery and started again. He got into the pötte hard, but he came! Smoked like a chimney in the back, coughed like a fool, and suddenly he ran silk soft again. Now this error is due to the weak battery, because when starting without proper current, the injection/detonation rises out, or this symptom indicates eventl. Announcement of greater damage ?? Would be a pity, since I actually won the car in the few days quite dear and wanted to keep it longer !
Thank you in advance for your help, Greeting Andre