Yes, the Old Testament is God's Word just as much as the New Testament is; in fact, it was the only Bible that Jesus knew (since the New Testament hadn't yet been written). The Bible says, "All Scripture is God-breathed and is useful" (2 Timothy 3:16, emphasis added).
I don't think it's accurate, however, to say that Christians ignore the Old Testament. The book of Psalms, for example, is a treasured part of every Christian's Bible. The same could be said of other parts of the Old Testament, such as Proverbs or some of the prophets. For many years I made it a practice to read five Psalms and one chapter of Proverbs every day, enabling me to read through those two books each month.
Nevertheless, I suspect you're right, up to a point; much of the Old Testament probably does get ignored -- and that's unfortunate, for God has many riches to share with us in its pages. The early chapters of Genesis, for example, set the stage for everything that follows, including our need for redemption. The prophets and historical books demonstrate how God deals with the human race. The Bible says, "These things happened to them as examples and were written down as warnings for us" (1 Corinthians 10:11).
Never forget: Jesus Christ is the center of God's Word, for through faith in Him we can be forgiven and cleansed of our sins. But God also wants to teach us how to walk with Him and serve Him, and He's given us the whole Bible to help us.