If you use Windows2000 or XP on your Athlon machine you can use LEC Quick And Easy (
http://www.lucasforums.com/showthread.php?s=&threadid=79875) to play old Lucasarts games.
Even if you dont you can still use ScummVM (
http://scummvm.sourceforge.net/) if you need a frontend for it you could use mine ScummVM Quick And Easy (
http://www.gorman.btinternet.co.uk/ScummVMQuickAndEasy1.1.zip)
Right, thats the pimping over now to see about fixing your actual problem.
I'm presuming here that you have one of the original versions of MI1 not one of the cd versions with audio as cd tracks.
Try starting with command line 'monkey1.exe v a' or similar. Theres not an awful lot I can do to help you here since things are dependant on your sound driver.
Type 'monkey.exe /?' to see the command line options and try starting with different combinations of them.
Its all a bit of a cop-out really, just play it with ScummVM on your new computer.