Installing SP4 via Group Policy

I am having problems installing SP4 via Group Policy.

All servers and DCs are Windows 2000 Server.  All workstations are
2000 Pro.  Single AD domain.  All workstations are members of the
Domain Computers group.

I downloaded SP4 to a network share and extracted it to the same
share.  Gave the Domain Computers Read share permission and Read,
Execute, and List Folder Contents file permissions.  Gave
Authenticated Users the same permissions and Domain Admins Full
Control.  (I'm not using DFS.)

Created a Group Policy linked to the appropriate OU.  Gave Domain
Computers and Authenticated Users Read and Apply Group Policy
permissions.

In the policy I went to Computer Configuration-->Software
Settings-->Software Installation.  Went to New-->Package and browsed
to the location of the Update.msi file in the SP4 share.  Made sure
the package was set to Assigned.

When the clients boot up, it looks like SP4 is going to be installed,
but then it never does.  Event Viewer shows an Event ID 102: "The
installation source for this product is not available".

KB article 278472 seems to indicate that this is a permissions issue,
but it looks like the permissions are set correctly as far as I can
tell.

Article 815438 doesn't apply because all the clients are currently at
SP2.

Does anyone else have any suggestions?

Thanks.