I successfully installed this forest:

Install-ADDSForest `
-DomainName "mysite.com" `
...
-NoRebootOnCompletion

I tried to install this domaincontroller:

Import-Module ADDSDeployment
Install-ADDSDomainController `
-DomainName "mysite.com" `
-CreateDnsDelegation `
-AllowDomainControllerReinstall `
-InstallDns `
-NoRebootOnCompletion

I got this error code:

Verification of user credential permissions failed. An Active Directory domain controller for the domain "mysite.com" could not be contacted. Ensure that you supplied the correct DNS domain name.

I tried adding -Credential $credentials with :

$Username  = "Administrator"
$SecurePassword  = ConvertTo-SecureString "@#PaSsWoRd" -Asplaintext -Force
$credentials = New-Object System.Management.Automation.PSCredential($Username, $SecurePassword)

Philosophi,

See. I have good character. Feel free to borrow it.

Isaac would have loved this.

When something cannot be contacted it usually means that the object is not available on the port/protocol specified.  You haven't connected so credentials don't count.

Try: "ping mysite.com"

Does it ping?  No.  Fix that. You may have DNS issues., router issues, other net issues.

This is how you make your bones; troubleshooting weird problems. 

Newton loved this stuff - so do I.