cross domain connectivity problem

I am the tech at a high school in a large city. Our city school district
has two domains, admin and student. In the downtown office, there's a
couple of domain controllers for each domain. In my school I have file
servers for each domain. It's all 2003 AD. The workstations at my school
are a mix of 2000 and XP.

From my single nic admin side workstation, I'm supposed to be able to
connect to student and admin computers. I can't. I can successfully

-ping both servers by name and ip
-ping admin work stations by name and ip
-ping student workstations in OTHER schools by name and ip
-nbstat -a to student workstation in my school.

However, if I ping a student workstation in my school by name, my computer
resolves the ip address but then, all I get is request timed out.
I have a static ip address. I have entires for the two admin side and two
student side dns and wins servers. My dns suffix is set to admin.x.x.x.
The same thing happens when I try to ping my school's student stations from
computers in other schools. This also happens from the computer of our
downtown tech who is responsible for network configuration. He's helping me
with the problem, but I thought I'd run it by this group.

Some things I have tried are:

-Creating a student side GPO to make sure no student xp boxes have firewall
blocking ports.
-ipconfig /flushdns and ipconfig /registerdns
-playing around with the arp and nbtstat commands.

For now, I've put a second nic in my machine that's on the student side.
But, obviously, that's not a long term solution.

I don't think it's a workstation specific thing though because other schools
can't get through either.So my question to you guys is where do you think we
should start troubleshooting:

-the configuration of switches and routers?
-bad cabling?
-dns and wins server setup errors
-GPO
-some setting on one of the file servers
-cross domain connectivity rules that our downtown network guy sets up
between the two subnets?

Thanks,
Jeremy