The situation of Rome at that time was entirely different than what you imagine. The first key thing to understand is that the western empire and eastern empire were split on political, ethnic and religious lines. The main power in the world (until 408) was Theodosius, the emperor in Constantinople. Constantinople was founded by the first Christian emperor, Constantine, and was thoroughly Christian and had a stable government. The emperors in Constantinople, including Theodosius, had an antagonistic relationship with Rome, which was half Christian, half pagan. In the 4th century Rome became increasingly chaotic and ungovernable with large mobs of poor people, wealthy decadent pagan Romans, foreign soldiers and other strange elements in a huge seething mass. Out of this chaos, an unknown named Eugenius was put forward as the western "emperor" in 392, defying the rule of Theodosius. The various Frankish barbarians then holding sway in Rome, who were pagans, had sponsored this revolt. Theodosius duly took an army and crushed them in battle in 394, installing his juvenile son, Honorius, as the titular ruler of Rome. Real power was wielded by the Vandal general Stilicho who was the head of the foederati, the German mercenaries loyal to the Roman empire. Note that these were Christian barbarians, unlike the Frankish barbarians in Rome who were pagans.
Stilicho gathered the remnants of the government who still supported Constantinople and moved them along with Honorius to Ravenna, a large military base which had a good port. There, they set up a rump government of the west which had very little control of Rome and absolutely no control of the rest of the western empire (Gaul, Iberia, Britain, etc).
This precarious status quo held for 14 years, but when Theodosius' son Arcadius died in 408 everything collapsed. The fawning courtiers surrounding Honorius intrigued against Stilicho and had him murdered. Honorius himself was useless, a spoiled 26-year-old brat. Pagan Romans and westerners took this as a signal to overthrow the now-leaderless foederati who were Constantinople's only forces in Italy. They went around massacring foederati and their families. The remaining foederati then fled to Alaric, the Visigoth, who was a Christian and loosely aligned with Constantinople. Alaric, now with the full support of the Italian foederati (Constantinople's warriors) and the moral high ground, descended on pagan Rome and sacked it.
As far as Honorius was concerned the pagan Romans, especially those in the countryside, were now getting what they deserved. The western pagan/Frankish legions in Gaul probably sympathized with their allies in Rome, but they were too weak, disunified and far away to do anything about it.