In our case, this problem was caused by an overzealous case of server hardening. In the Local Security Policy, under Local Policies -> User Rights Assignment, an admin had removed "Users" from those groups listed in "Bypass Traverse Checking". I added the Users group back to this list, rebooted, and this problem (and several others) was resolved.
An engineer changed permissions on C:\WINNT from Everyone:Full Control to Everyone:Read, but failed to add in Administrators, System account, and other appropriate groups. When MSDTC starts, it writes a file to c:\winnt. In this case, having read-only permissions prevented it from starting. Followed by Event 4111 - The MS DTC Service is shutting down.
In my case, the cluster service did not start correctly. Restart Cluster service, then the MTS starts without problems.
As per ME223397
, this may occur if the Microsoft Distributed Transaction Coordinator (MSDTC) is not properly installed or is malfunctioning on one or both nodes on the Cluster Server computer. See the Q article for resolution.