ddub85,
Dispensational theology in my opinion confuses covenants, dispensations, law and gospel. Depending on which version of dispensationalism you are dealing with, you'll get different answers to this question, I believe. Although I am not an expert on covenant theology, structurally, it is very simple.
As you know there are three overarching covenants, Redemption, Works, and Grace. The covenant of redemption does not include man. The other two covenants are with man. The covenants that are commonly referred to such as the Abrahamic, Noahic, Mosaic, Davidic, New, etc., fit in one or both covenants of Works and Grace.
Also, the distinction between "Law" and "Gospel" is a very important hemeneutical distinction in order to understand Covenant Theology and Reformational theology in general. A rough definition of these terms is that Law stands for everything God demands from mankind (not just the OT, since there is Law in the NT). Gospel is every promise that God makes to mankind, i.e., what He graciously provides on our behalf.
I don't know exactly what you mean that you can't find anything in the bible to support that we're under the new covenant. The new covenant was prophesied by Jeremiah and established by Christ. If you're a believer you're part of the new covenant. The old covenant is generally a reference to the Mosaic Covenant which in Hebrews we're told is obsolete and fading away.
IMO, the old covenant has been abrogated fully and finally at Christ's death and resurrection. So, even though the Jews continued to offer sacrifices until 70 A.D., the covenant under which they operated was no longer in force. It had been fulfilled by Christ. (He came to fulfill the Law and the Prophets.)
Blessings,
aL
