Database corruption problem?
If its that there is a workaround with Tier III involvement
I would say that apparently nothing is listening (or the communication is blocked) on the port that is specified in Groupshield as MQM listen port. Please check port assignments and perhaps if any firewall, etc. is not blocking this communication (even local Virusscan on the Exchange or MQM server).
Has this MQM ever worked for you prior to this failure in the same implementation?
For similar hard times with MQM 7 see this help: https://kc.mcafee.com/corporate/index?page=content&cat=CORP_QUARANTINE_MANAGER_7 _0&channel=CORP_KNOWLEDGEBASE