Consider using ordinary least squares, where as you've specified, column D is the outcome variable. This would be a basic equation you are modeling, with no interactions:
$D=\beta_1 A+\beta_2 B_B+\beta_3 B_C+\beta_4C$
The $\beta$s give you the relationship between each variable and D, independent of the other variables in the model. I'm treating A as continuous - it is ordinal, but with 7 levels - you can often treat that roughly as continuous. It is not always appropriate, but it could initially identify a relationship. You could alternatively include each level of A, like I've done with C but it get's a little messier. Also notice I've left out $B_A$ - that is for identification purposes and you cold just as well choose a different level to omit. $\beta_2$ and $\beta_3$ represent the average difference between $B_A$, and $B_B$ and $B_C$, respectively.
Now, if you have reason to believe that the relationship between A and D, or C and D depends on the level of B (which it sounds like you might), you can approach the modeling different ways. One way would be to include interaction effects between each of the levels of B and A and C, as such:
$D=\beta_1 A+\beta_2 B_B+\beta_3 B_C+\beta_4C+\beta_5 B_B*C+\beta_6 B_C*C$
In this case, the coefficients $\beta_5$ and $\beta_6$ represent the difference in the relationship of C depending on the level of B. This model, as well as the initial model, assume the relationships between D and A and C are linear. If you do not believe they are linear, you can include polynomial terms, though keep in mind that gets more complicated to interpret, particularly with interactions.
Another alternative would be to run initial model above on all three subgroups of B, and then compare the coefficients across the three models. I'm not familiar with JMP to know how this may be done, but in a program like R or Stata this can be done fairly easily. Keep in mind, these results hold for dependent variables that are continuous. If your dependent variable is not continuous, or you are looking at nonlinear models, then it gets much more complicated.