If you have "tasklist", here is an easy way to do it:
Code:
$sProcess="notepad.exe"
 
Shell '"'+%COMSPEC%+'" /C '
	+'tasklist /FI "USERNAME eq '+@USERID
	+'" /FI  "IMAGENAME eq '+$sProcess+'" /NH | FIND "No tasks" >NUL:'
If @ERROR
	"Already running an instance of '"+$sProcess+"'"+@CRLF
Else
	"No '"+$sProcess+"' running for this user, so I'll start one now..."+@CRLF
	Run $sProcess
EndIf