Windows – FSMO-owner not replicating

I have an Active Directory with 6 DCs, where the newly added DC02 is not replicating. It's a mixed environment from Windows 2003
It is also the owner of PDC, RID and Infrastructure roles.
Now I'm wondering what the best way to move forward is.

The new DC is replacing a demoted DC with a different name, and initially everything looked okay with the new one after it was added. I let it sit for about a week after promoting it, to let it finish all replication before moving the FSMO-roles over. It didn't give me any fuss about transferring the roles over, so I assumed it was all working as intended. After a while we started noticing that new DNS-records added to DC02 wasn't replicated to the other DCs.

From what I can tell, the situation now is as follows:

• DC02 does not have SYSVOL and NETLOGON shared
• The other DCs are still seemingly replicating amongst eachother, but none have a connection to DC02. DC02receives updates from the other DCs
• Other DCs report an ERROR for the role holder of PDC, RID, and Infrastructure

From my reseach, I'm thinking I have two options, and wondering which would be the best to use:

1. A D2/D4 Burflags authoritative restore, setting D4 on a working DC and D2 on the DC02 (and all the other DCs?).
   I've not done this before, and feel tentative as I'm not really sure what it will do.
2. Taking the faulty DC02 offline permanently and Seize the FSMO-roles back to the original DC. Not really sure what this would do either.

I'd appreciate any tips on how to move forward, and which precautions might be necessary.

Update 1:

The old FSMO-owner DC01 gives this when running a dcdiag
Is it safe to assume these errors are caused by the faulty DC, and should still be okay to tranfer back the roles to this server?

dcdiag /q:

Dcdiag could not locate (null) in the dcdiag's cache of servers. Try
running this dcdiag test against this server, to avoid any problems
caused by replication latency.
......................... DC01 failed test RidManager
An Warning Event occured. EventID: 0x8000072D
Time Generated: 09/14/2016 14:11:57
(Event String could not be retrieved)
......................... DC01 failed test kccevent
An Error Event occured. EventID: 0x40000004
Time Generated: 09/14/2016 13:32:33
Event String: The kerberos client received a
An Error Event occured. EventID: 0xC000001B
Time Generated: 09/14/2016 14:01:07
Event String: While processing a TGS request for the target
An Error Event occured. EventID: 0x40000004
Time Generated: 09/14/2016 14:01:15
Event String: The kerberos client received a
......................... DC01 failed test systemlog
Warning: DcGetDcName(PDC_REQUIRED) call failed, error 1355
A Primary Domain Controller could not be located.
The server holding the PDC role is down.
......................... domain.com failed test FsmoCheck

Netdom query fsmo:

Schema owner DC01.domain.com
Domain role owner DC01.domain.com
The parameter is incorrect.
Try "NETDOM HELP" for more information