After Migration Exchange 2010 to 2013. And uninstall Exchange 2010 from the directory I can not install another exchange for below error. 
Error:
The following error was generated when "$error.Clear(); 
          if (($RoleIsDatacenter -ne $true) -and ($RoleIsDatacenterDedicated -ne $true))
          {
            if (test-ExchangeServersWriteAccess -DomainController $RoleDomainController -ErrorAction SilentlyContinue)
            {
              # upgrade the discovery mailboxes to R5 version, this will fix the RecipientDisplayType property of the discovery mailbox which was wrong in R4.
              get-mailbox -RecipientTypeDetails DiscoveryMailbox -DomainController $RoleDomainController | where {$_.IsValid -eq $false} | set-mailbox -DomainController $RoleDomainController
              $name = [Microsoft.Exchange.Management.RecipientTasks.EnableMailbox]::DiscoveryMailboxUniqueName;
              $dispname = [Microsoft.Exchange.Management.RecipientTasks.EnableMailbox]::DiscoveryMailboxDisplayName;
              $mbxs = @( get-mailbox -Filter {name -eq $name} -IgnoreDefaultScope -resultSize 1 );
              if ( $mbxs.length -eq 0) 
              {
                $dbs = @(get-MailboxDatabase -Server:$RoleFqdnOrName -DomainController $RoleDomainController);
                if($dbs.Length -ne 0) 
                {
                  $mbxUser = @(get-user -Filter {name -eq $name} -IgnoreDefaultScope -ResultSize 1);
                  if ($mbxUser.Length -ne 0) 
                  {
                    enable-mailbox -Discovery -identity $mbxUser[0] -DisplayName $dispname -database $dbs[0].Identity;
                  }
                }
              }
            }
            else
            {
              write-exchangesetuplog -info "Skipping creating Discovery Search Mailbox because of insufficient permission."
            }  
          }
        " was run: "Database is mandatory on UserMailbox.".

Error:
The following error was generated when "$error.Clear(); 
          if (($RoleIsDatacenter -ne $true) -and ($RoleIsDatacenterDedicated -ne $true))
          {
            if (test-ExchangeServersWriteAccess -DomainController $RoleDomainController -ErrorAction SilentlyContinue)
            {
              # upgrade the discovery mailboxes to R5 version, this will fix the RecipientDisplayType property of the discovery mailbox which was wrong in R4.
              get-mailbox -RecipientTypeDetails DiscoveryMailbox -DomainController $RoleDomainController | where {$_.IsValid -eq $false} | set-mailbox -DomainController $RoleDomainController
              $name = [Microsoft.Exchange.Management.RecipientTasks.EnableMailbox]::DiscoveryMailboxUniqueName;
              $dispname = [Microsoft.Exchange.Management.RecipientTasks.EnableMailbox]::DiscoveryMailboxDisplayName;
              $mbxs = @( get-mailbox -Filter {name -eq $name} -IgnoreDefaultScope -resultSize 1 );
              if ( $mbxs.length -eq 0) 
              {
                $dbs = @(get-MailboxDatabase -Server:$RoleFqdnOrName -DomainController $RoleDomainController);
                if($dbs.Length -ne 0) 
                {
                  $mbxUser = @(get-user -Filter {name -eq $name} -IgnoreDefaultScope -ResultSize 1);
                  if ($mbxUser.Length -ne 0) 
                  {
                    enable-mailbox -Discovery -identity $mbxUser[0] -DisplayName $dispname -database $dbs[0].Identity;
                  }
                }
              }
            }
            else
            {
              write-exchangesetuplog -info "Skipping creating Discovery Search Mailbox because of insufficient permission."
            }  
          }
        " was run: "Database is mandatory on UserMailbox.".

Hello

tip: http://goo.gl/kLmfbq http://goo.gl/4c2W

First Reset the Password DiscoverySearchMailbox and go to Exchange Management Shell and Enter the below commend.

Disable-Mailbox -identity "DiscoverySearchMailbox {D919BA05-46A6-415f-80AD-7E09334BB852}" 

Special Thanks: Sneff Gabor..

Hello,

Many times the un-installation of old Exchange server creates such problem. So if you want do quick, error and hassle free migration from old Exchange to new Exchange Server then you should try an automated tool. I would like to recommend you one of the tested tool by myself in my Exchange lab i.e. http://www.lepide.com/exchangemigrator/. 

Hopefully it will help you do easy migration from Exchange to Exchange including Public folder and Intra-Cross forest migration between two exchange.

Walter