One of the reasons we shouldn't neglect the Old Testament is because we can not understand the New Testament without it. Every book of the New Testament contains quotations from and allusions to the Old Testament. I am not talking about merely mentioning stories, although New Testament writers articulate theology using the Old Testament. The book of Revelation is a case in point.
No other book in the New Testament is as thoroughly saturated with the Old Testament as the book of Revelation. The book draws upon the Old Testament hundreds of times. While certain books were particularly influential (Daniel, Isaiah, Zechariah, Ezekiel), the apostle John essentially considered the entire Old Testament as a source for his book.
The dominant influence of the Old Testament may seem surprising. One reason is that John often does not preface his use of the Old Testament with formulaic phrases like "thus says the Lord" or "as it is written." Instead, John embeds Old Testament material directly into his scenes, visions, and angelic revelations. He presumed his readers would be so literate with respect to Old Testament content that telegraphing when he wove it into his work wasn't necessary.
One of the questions John's use of the Old Testament has generated among students of his work is whether he is faithful to the original context of the material he quotes. The question arises from passages like Revelation 5, where John combines creaturely imagery from both Daniel and Ezekiel in his vision of the four beasts (Daniel 7) "full of eyes" (the wheels of Ezekiel 1). Is John just "doing his own thing" with the Old Testament?
John doesn't ignore the original meaning of these and the other passages he cites from the Old Testament. He is fully aware of the original contexts. Rather, he applies the Old Testament material (words, phrases, symbols, metaphors, etc.) to new apocalyptic messaging in his own work.
What all this means is that the key to interpreting the New Testament is not the newspaper; it is the Old Testament. No one can claim to understand the Book of Revelation without a thorough grasp of the Old Testament passages John quotes or alludes to. Those Old Testament passages must first be understood within their original contexts and ancient worldviews. Only with that framework in hand is anything John says or describes in the least way comprehensible. The neglect of the Old Testament is one reason why nearly all of what it says is a complete mystery to those who read it.