What we want to do

I want to setup a private virtual lab on my hyper-v host (HOST). We currently run Exchange Server 2007 SP3 on our email server and plan to upgrade it to Exchange Server 2013. My team wants to test the upgrade process before rolling out production. We want to have a lab on HOST using a Private Switch in Hyper-V 2012 (Windows Server 2012 server only running Hyper-V role). In the lab we want to have our Exchange Server 2007 SP3 email server, a DC holding all FSMO roles, and a workstation running office to test email functionality.

What we have tried

We setup HOST with a private switch. Using Veeam BR, we successfully replicated our email server and DC to HOST. Both VMs had their correct IP configurations and able to ping each other. At first, Exchange even worked (worked meaning, in the mgmt console all the mailboxes and settings were there and right), SYSVOL shares were searchable, and everything was good. That only lasted a few minutes. After a few minutes ping was all that worked. Network shares weren't reachable. Exchange couldn't find the DC.

On the DC, AD wasn't happy. I saw various errors for the RPC server unavailable, ADWS can't be reached, and a primary DC cannot be found.

Reboots of both VMs didn't fix anything. Blowing the VMs away and replicating VMs back to HOST resulted in the same thing: things work for a few minutes and then, I only assume this, Active Directory goes awry. I assume DNS isn't the problem since from both VMs I can ping the hostname? Any suggestions?

Thanks!

update 9/1/2015 Email VM has DC\DNS server as its primary DNS server. DC\DNS looks to itself for primary DNS.

Running Get-ADComputer -identity (name of email server) returns the following Red text

Get-ADComputer: Unable to find a default server with Active Directory Web Services running.

ADWS is running on my DC\DNS server.

EDIT to show troubleshooting steps taken Per longneck's suggestion I did seize all of the roles to the DC. However, AD still isn't working for my lab VMs. DNS is working, but AD isn't. Both VMs have Public status for their NICs. Even after changing to Private AD isn't working. The GUI tools for AD won't work because a Domain can't be contacted. I assumed it is because we have other sites (our branch offices). Obviously replication won't work because the DC can't contact the partners. So using NTDSUtil I deleted the other DCs. Doing a reboot after DC removal, still no dice. Also, I found the SYSVOL and NETLOGON shares won't share. I tried the first two suggestions from this link http://www.eventid.net/display.asp?eventid=13559&eventno=657&source=NtFrs&phase=1 but still AD doesn't work.

9/2/2015 UPDATE

I am throwing in the towel on this one. I will create a new domain on some VMs in our lab and use the domain just for testing. I am not sure why AD wouldn't work in my setup, but it wouldn't. If things weren't wonky, I am sure longneck and joeqwerty's answers would have worked.