OK....here I am.
We recently went thru a NT4 to 2K3 migration.
I described a little in this thread:
http://www.techzonez.com/forums/showthread.php?t=10224
You will need 2 computers to use temporaly, but it is worth it, REALLY worth it.
Our move also included at the same time moving from Exchange 5.5 to 2003, so it was a bit more complicated.
Kerberos could as pointed out be your problem. If you need, I can take note of the kerberos settings we used.
We are still working in mixed mode for the moment, since our Domain server is a file server, and the backup domain server is the printer server and NT doesn't have any *demote* function, but pretty much serving from the 2K3.
The Domain name I don't understand what is your problem, thought at the same time it is a problem.
We basically are running the system with 2 domains which are one. The NT4 Domain name, and the 2K3 domain name. For 2K3 it is better to use a domain name that is standard with a DNS entry, since it will be resolved thru DNS, so, for example, one of our DNS is TechZ (for NT4) and the new one is actually techzonez.int (int to refer as internal, since we have a web site .com) I don't really remember now why, but it made lots of sense at the moment
So, inside the LAN you can be either connected to TechZ or Techzonez.int. Windows 2K and up usually connect to the int, but NT likes the other one. That is for the domain name. Since you said the administrator wanted to keep the same domain name, I am asuming that you are a contractor, or, working on the side. IF that it is the case, you should present the admin with the advantages and make a case for them. IF they still decide to do it their way, at least you told them so
In my case I am the admin, but I am usually the one that request the improvements when we have a contractor (They do hate me so much, because I really do make them work)
As for the method described on the link, one NT4 (new installation) is used for backup, before the upgrade (In your case, it is better to turn off the 2K3 server while sinchronizing). The other you upgrade to W2K3 and that will pass the settings to your REAL W2K3, but before that, you turn off the NT4 server, that way you have the domain runnin on real W2K3 mode, with all the settings from NT4. This is not as easy as it sounds, but it provides a better ground to work. Also, NT4 because it is old, it is actually a lot harder to install, because it doesn't recognize a lot of hardware. We had problems with 6 computers because it won't work with their NICs. Finally some old PIII 500 Mhz did the trick.
For the user running W98, get him upgraded to W2K. IT is 200$ on licence (XP will run too, but for Domain get PRO), but he will get back the ROI in stability and features.
You defenitively don't want a W98 in a Domain, they are your points of entry for Virus, worms, backdoor and all kind of trouble (not to mention crashing, and data corruption).
Finally, NT4 uses directory Services. Active Directory was introduced with Windows 2000. Directory Services is a LOT easier to use, but provides a lot less flexibility and features.
Also, Active Directory is a lot more friendly to centralized, remote management. We did most of the migration upgrade thru the AD tools installed in a user computer instead of working on the server. You want to avoid working on the server as much as you can