Why would this Semidefinite Program be Dual Infeasible?
The original poster seems to misunderstand the distinction between "primal infeasible" and "dual infeasible."  

The output from CSDP shows that the problem is primal feasible ($X=0$ is a primal feasible solution) but that the primal problem is unbounded. By weak duality, the corresponding dual problem is infeasible.   

If you just want a primal feasible solution and don't care about the primal objective value, then you can get this in a couple of ways:


You can use the "certificate" returned by CSDP.  This is a matrix $X$ such that $X$ is positive semidefinite and $A(X)=0$.  Any positive multiple of this matrix is a primal feasible solution to your SDP.  
You can add an additional constraint that causes the objective function to be bounded.  A simple choice would be trace(X)=100.   


By the way, it's easy to confirm this using another SDP solver such as SeDuMi or SDPT3 or SDPA.