Cannot access admin shares on a domain controller from another domain controller without entering credentials again

Can you do an netdiag then post the results. You aren't getting any errors in the Event log, right?

Netdiag results:

    Computer Name: GEIDIPRIME
    DNS Host Name: geidiprime.towerdigital.ad
    System info : Windows 2000 Server (Build 3790)
    Processor : x86 Family 15 Model 3 Stepping 4, GenuineIntel
 
Netcard queries test . . . . . . . : Passed
    [WARNING] The net card 'RAS Async Adapter' may not be working because it has not received any packets.
    [WARNING] The net card 'SSL-VPN NetExtender Adapter' may not be working because it has not received any packets.

Per interface results:

    Adapter : Local Area Connection

        Netcard queries test . . . : Passed

        Host Name. . . . . . . . . : geidiprime.towerdigital.ad
        IP Address . . . . . . . . : 10.2.0.100
        Subnet Mask. . . . . . . . : 255.255.255.0
        Default Gateway. . . . . . : 10.2.0.1
        Dns Servers. . . . . . . . : 10.2.0.101
                                     10.2.0.100

        AutoConfiguration results. . . . . . : Passed

        Default gateway test . . . : Passed

        NetBT name test. . . . . . : Passed
        [WARNING] At least one of the <00> 'WorkStation Service', <03> 'Messenger Service', <20> 'WINS' names is missing.

        WINS service test. . . . . : Skipped
            There are no WINS servers configured for this interface.

Global results:

Domain membership test . . . . . . : Passed

NetBT transports test. . . . . . . : Passed
    List of NetBt transports currently configured:
        NetBT_Tcpip_{703524EE-2254-417E-B311-5D6BE9AF4B5C}
    1 NetBt transport currently configured.

Autonet address test . . . . . . . : Passed

IP loopback ping test. . . . . . . : Passed

Default gateway test . . . . . . . : Passed

NetBT name test. . . . . . . . . . : Passed
    [WARNING] You don't have a single interface with the <00> 'WorkStation Service', <03> 'Messenger Service', <20> 'WINS' names defined.

Winsock test . . . . . . . . . . . : Passed

DNS test . . . . . . . . . . . . . : Passed
    PASS - All the DNS entries for DC are registered on DNS server '10.2.0.101' and other DCs also have some of the names registered.
    PASS - All the DNS entries for DC are registered on DNS server '10.2.0.100' and other DCs also have some of the names registered.

Redir and Browser test . . . . . . : Passed
    List of NetBt transports currently bound to the Redir
        NetBT_Tcpip_{703524EE-2254-417E-B311-5D6BE9AF4B5C}
    The redir is bound to 1 NetBt transport.

    List of NetBt transports currently bound to the browser
        NetBT_Tcpip_{703524EE-2254-417E-B311-5D6BE9AF4B5C}
    The browser is bound to 1 NetBt transport.

DC discovery test. . . . . . . . . : Passed

DC list test . . . . . . . . . . . : Passed

Trust relationship test. . . . . . : Passed
    Secure channel for domain 'TOWERDIGITAL' is to '\\arrakis.towerdigital.ad'.

Kerberos test. . . . . . . . . . . : Passed

LDAP test. . . . . . . . . . . . . : Passed

Bindings test. . . . . . . . . . . : Passed

WAN configuration test . . . . . . : Skipped
No active remote access connections.

Modem diagnostics test . . . . . . : Passed

IP Security test . . . . . . . . . : Skipped

Everything looks good. Are you logging into the servers with the same user? Are you sure there isn't anything in the Event Logs at all? Are you logging on the server as the domain or local?

Yes, logging in as the Domain Admin. Since both are DC's, you can only log into the domain.

Try to see if you can reset the secure channel.

https://www.experts-exchange.com/questions/23629068/Computers-in-NEtwork-lose-Domain-connection-randomly.html

Is this wise on a domain controller?

This is fine.

http://support.microsoft.com/kb/325850

Also, when I run an "nltest" on each domain controller, DC1 works fine and DC2 gives me the following error:

C:\>nltest /server:ARRAKIS /sc_query:towerdigital.ad
I_NetLogonControl failed: Status = 1355 0x54b ERROR_NO_SUCH_DOMAIN

I ran the "Netdom" tool and it had an error on DC2:

C:\Program Files\Support Tools>netdom resetpwd /s:GEIDIRPIME /ud:towerdigital\ad
ministrator /pd:*
Type the password associated with the domain user:

The machine account password for the local machine could not be reset.

The network path was not found.

The command failed to complete successfully.

Did you run the netdiag on the DC having trouble?

NLTEST now works after resetting the machine passwords properly on the 2 DC's. I still have the original issue though. Here is th eoutput from the following command:

C:\Program Files\Support Tools>REPADMIN /SHOWCONN ARRAKIS
Base DN: CN=Default-First-Site-Name,CN=Sites,CN=Configuration,DC=towerdigital,DC
=ad
==== KCC CONNECTION OBJECTS ============================================
Connection --
    Connection name : 30472b15-6575-4b09-bdca-b8c452efbbc5
    Server DNS name : arrakis.towerdigital.ad
    Server DN  name : CN=NTDS Settings,CN=ARRAKIS,CN=Servers,CN=Default-First-Si
te-Name,CN=Sites,CN=Configuration,DC=towerdigital,DC=ad
DsReplicaGetInfo() failed with status 8453 (0x2105):
    Replication access was denied.
DsReplicaGetInfo() failed with status 8453 (0x2105):
    Replication access was denied.
       
Note that it fails due to access denied.

You are not getting any errors in the Event Logs? Usually this is because the server isn't connected to the domain or doesn't have the secure channel password. Run a netdiag then post for me