hmm, I am assuming that you are storing the batch script you are trying to run in the netlogon folder and Server4 is your primary domain controller.
if this is your script, then try and add "Pause" without quotes at the end of it. This just pauses the script and waits for user action. If nothing shows up then i can figure out further what your problem is. The netlogon share should allow you run batch scripts regards less if they are admin or not.
net use n: \\server1\users\students\%username% /persistent:no
net use o: \\server3\applications /persistent:no
NET TIME \\server4 /SET /YES
if exist \\server4\netlogon\screenres\%computername%.bat call \\server4\netlogon\screenres\%computername%.bat
if not exist \\server4\netlogon\screenres\%computername%.bat call \\server4\netlogon\screenres\default.bat
reg delete "HKCU\printers\connections" /f
if exist \\server4\netlogon\printers\%computername%.reg regedit /s \\server4\netlogon\printers\%computername%.reg
if not exist \\server4\netlogon\printers\%computername%.reg regedit /s \\server4\netlogon\printers\allprinters.reg