The log file under %systemroot%\system32\msdtc had become corrupted.
We were seeing another message saying:
MS DTC log file not found. After ensuring that all Resource Managers coordinated by MS DTC have no indoubt transactions, please run msdtc -resetlog to create the log file.
So we cleared out the windows\system32\MSDTC folder and ran msdtc -resetlog which then started.
We also saw:
MS DTC started with the following settings:
Security Configuration (OFF = 0 and ON = 1):
Network Administration of Transactions = 0,
Network Clients = 0,
Inbound Distributed Transactions using Native MSDTC Protocol = 0,
Outbound Distributed Transactions using Native MSDTC Protocol = 0,
Transaction Internet Protocol (TIP) = 0,
XA Transactions = 0
In the log following the start-up.