MQ Server service would start but I could not open the MQ Series Explorer snap-in. Making MQ Series work did not involve changing the Service to run under a domain account; I have left the Service (IBM MQSeries) running under LOCAL SYSTEM.
To fix the problem, I had to open DCOMCNFG and modify things here. First, setup a user account in the Windows Domain that is a member of the Domain User group Domain MQM group and Global MQM group. The user account does not need Administrative rights to the domain nor the server itself. Next, open DCOMCNFG on the MQSeries server, on the Applications tab select IBM MQSeries Services, and then choose Properties. Select the Identity tab. In the "Which user account do you want to use to run this application" section choose This User and then browse the Domain and select the user account you just created. Type in the password for the user account and click OK. Then go back to Services and restart the IBM MQSeries Service. This fixed the problem for me.