I'm confused, you are saying you can start the car just fine, but not with the remote starter?

Is the engine cranking but not starting if you use the new remote starter?

This is what would happen with an unauthorized start attempt.
If nothing was done when installing the remote starter to address the presence of the DAS system, the remote start will not work.
Try putting a spare key into the ignition switch and see if the remote starter will work, i am doubting that will work though, unless the remote starter is wired in such a way that the DAS antenna is activated, and even then it would probably just work once (without removing and reinstalling the key) due to the rolling code feature.
You may be able to rig up one of these key-holder boxes that are used for example on GM vehicles with the "Theftlok" system.

Again, this is a very integrated system, there is no "silver bullet" or simply a few wires you can disconnect, it's more complex than that. I think you're going to have to "work with" this DAS system, not simply disable the anti-theft system. You think you're fighting the anti-theft system, but you're not, you're fighting the DAS system. The DAS is recognizing the unauthorized start attempt and setting off the alarm, and you can't simply tell the DAS to not do that, you're going to have to "convince" DAS that the start attempt is authorized. If you don't "convince" DAS to not set off the alarm, it's also not going to allow the engine to start with the remote starter.

Gilly