ASPExec is a pretty ancient component, created in the days of IIS 2 and IIS 3. Whether it still works with current versions of IIS is anybody's guess.
You'd probably be better off just using the MS WSH shell.
Something like this:
Set oShell = Server.CreateObject("Wscript.Shell")
oShell.Run "C:\Premier12\myobp.exe \\melbdcsql02\company\myob\MYOB Premier\Premier 2008_09 Test.MYO"
Or you might need to prefix the call to the .exe with %ComSpec%
But I wouldn't expect any window to appear. Modern web servers don't want to allow apps to open windows on the server machine, for good reason.