Since it works on some machines and not on all, chances are good it’s not plugin or theme related. However, be sure to switch to twentyeleven and see if it’s working there, as sometimes theme authors will enqueue scripts like jQuery or TinyMCE from Google CDN, which would be disabled if there’s something (browser or OS) that’s disabling cross-site javascript loading.
Overall best guess: your client has something that is disabling javascript for him.
Solution 1: have your client disable all anti-virus or software-blocking programs (TeaTimer, etc) and check to see if it works again. Make sure Start -> Internet Options -> Security is not set to ‘high’.
If that doesn’t work, solution 2: have your client install FireBug and using Skype screenshare, LogMeIn, or Remote Desktop go into your client’s machine and see what’s happening for yourself. Chances are there’s a configuration setting that your client’s forgotten he set.
If you can’t figure it out from there, solution 3: have your client install a new browser – Opera is a great one for this, because very few people have installed it before, giving you a nice fresh start. Test in a vanilla browser install and see what happens.
Good luck!