Windows 2003 + Office 2003 Terminal Services problem!

I've had this problem for 2 months now, and tried everything, read everything and then rememebr my EE account, so I really hope I can fix the problem after this :)  I'm more than willing to increase the points to my current points total to anyone who can solve the problem.

Basically, at work, we have a single Windows 2003 Terminal Server running in Application Server Mode.  When I started, it never worked, and It was given to me to 'fix' and it had everything installed on it.

The problem is, when a normal Domain User logs in and tries to open a microsoft office application (word, outlook, visio, project..anything), they get an MSI error saying:

"Only administrators have permission to add, remove, or configure server software during a Terminal services remote session.  If you want to install ro configure software on the server, contact your network administrator."

Event log spits out event ID 1004, then 1001: (this is when the normal user tried to load Visio 2003)

Event ID: 1004:
Detection of product '{91510409-6000-11D3-8CFE-0150048383C9}', feature 'VisioCore', component '{45263A41-952C-4331-A44D-420BAB4E5C46}' failed.  The resource 'H:\Program Files\Common Files\Microsoft Shared\Visio Shared\VISFILT.DLL' does not exist.

Event ID: 1001:
Detection of product '{91510409-6000-11D3-8CFE-0150048383C9}', feature 'VisioCore' failed during request for component '{7E5F9F34-8EA7-4EA2-ABFB-CA4E742EFFA1}'

That is basically the problem I am having.  I have tried removing ALL office programs, and reinstalling it via the following method:
* Loged onto the server via mstsc.exe, and logged on as local administrator.
* removed all office programs (visio, project, office)
* reboot
* start menu -> add/remove programs -> add -> floppy/CD -> selected setup.exe in the network share we have of Office 2003.
* Put in Product Key, then while it was installing, it complained about H:/ missing!!!   Being a local admin, you don't have H:/ which is every users home directory mapping. (\\fileserver\home\<username>
* So I logged out, and logged in with my domain account, which is a Domain Adminstrator using mstsc.exe on my XP workstation.  
* Started setup same way, told it to do a "Complete" install, it installed fine (because H:/ existed.)
* Once it installed, It worked for me and everything worked (and currently still works)

Then tried to log in with our normal domain user test account, logged into it with mstsc.exe, logged in fine, but when I tried to run anything, I still got the same error as before.

Then it goes on...

For testing, I tried giving our normal domain user test account, local admin access of the box, and yes, MSIInstaller runs fine, starts installing components, BUT then FAILS with the "Microsoft Source Engine" error.   So I go into Services of the server, and Office Source Engine shows it's location as "H:\Program Files\Common Files\Microsoft Shared\Source Engine\OSE.EXE"

Thats basically it.  Something is SERIOUSLY wrong and it's beyond me, or I'm missing something blatantly obvious so I'm hoping you experts can help me :)

Seems to be that it's half installed into H:/ or something.   Is it fine to be installing office for ts, logged in via mstsc.exe, and not directly logged into the computer via the server KVM's?  Also, what does it mean when people say 'log in via console', I've heard it mentioned somewhere on here but didn't know exactly.  (I started unix, to me console is ssh/telnet, something which 2003 doesn't really have)

Every user in our domain is configured such that there "Profile" tab, "Home Folder" has H:/ mapped to \\fileserver\home\<username>, and Logon Script is "\\fileserver\home\login.bat" which merely does a couple file shares maps to Document Folders.  "Terminal Services Profile" tab is all empty, with "allow login to terminal server" enable,  and local path selected but the textfield beside it empty.

I'm crying out for help on this one!

Thanks.