The fall of Rome is usually considered to have occurred in 476 A.D. when the Western Empire was taken over by the barbarian King Odacer. Emperor of the Eastern Empire (Xeno) recognized Odacer as a legitimate ruler of the Western Empire therefore causing a debate of Rome's actual "fall."
As for falling in 800 AD, I suppose one could argue it "fell again" (the western empire) when Charlemagne was crowned Emperor of Rome (in 800 AD). Although there was already a crowned emperor of the western Roman Empire at the time, Pope Leo III decided to crown him anyway. This I guess this could be a reason someone would be able to argue that Rome fell again. I personally think the point in which it started to slowly deteriorate was in the aforementioned date 476 B.C. thus causing it to die out slowly as oppose to an exact date in which it "fell."
I'm no historian, just a history student and I hope this may help even if it is just a little bit. I'd site more sources, but I don't think you would care to look at the exact source I did because most sources give the facts that I gave.
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410 AD with the fall of Rome to 1400 with the start of exploration.
The fall of Rome in 410 AD
He sacked Rome, which was practically defunct by then.
410 AD with the fall of Rome to 1400. Lasted a 1,000 years.
Rome was 753 years old before AD