Bah! I must be blind!
{EDIT}
Alrighty, here's the output from the script, as is:
Code:

The computer OFF-SGONZALEZ responds to ping
OFF-SGONZALEZ is running SMBill.exe with a PID of: 2880
The computer OFF-SBERGER responds to pingSelect * from Win32_Process Where Name
= 'School.exe'Select * from Win32_Process Where Name = 'SMinder.exe'Select * fro
m Win32_Process Where Name = 'SMAdmin.exe'Select * from Win32_Process Where Name
= 'SMReport.exe'Select * from Win32_Process Where Name = 'SMBill.exe'Select * f
rom Win32_Process Where Name = 'Admission.exe'
The computer OFF-TSINGERY responds to ping
The computer OFF-FRONTDESK responds to ping
OFF-FRONTDESK is running School.exe with a PID of: 872


Soooooo, more or less, we're getting there. It may be that a great deal of the left out info would be displayed if I added some NET SEND messages. What do you guys think?