Some states do communicate with one another about a person's license status. In my experience, if your original state is one with which MA communicates, then the RMV will not issue you a driver's license until you clear up that matter. In your case, you are seeking only a MA id, so your out-of-state driving issues shouldn't have an impact.
The information provided here is not to be constituted as legal advice, and no attorney-client relationship is established.
Make sure you print out your proof that you've paid the tickets. If you have the money you can turn yourself in on the warrant and bond out, or hire an attorney to mile a motion to quash the warrant since you've paid the tickets.
This general legal advice does not create an attorney-client relationship. Every case is individual and to have legal advice that you can rely on you need to talk to an attorney one on one, answer their questions, and hire them.
If the warrant is cleared up, you should not have a problem getting a MA ID. The lack of a license should not prevent you from getting an ID. Then when you have paid all the money owed to the other state, you should be able to get a MA license.
If you do have problems getting the ID and/or license, there is an appeals process. You first appeal to a hearing officer, and if that does not result in a satisfactory resolution, you can appeal to the RMV Board of Appeals.
You should have no problem obtaining a Mass. ID Card, while in the meantime you resolve the issue from your home state and fix the warrant.
The Mass. RMV can be difficult to deal with, and in fact, they will likely not issue a driver's license until you pay the fines in your other state and he warrant is released.
Also - make sure you know the difference between applying for a new license, and transferring your out of state license to a Mass. License. If you apply for a new license, it may be a way around an intensive background check. Call the RMV for more details