Makaveli213 is correct. There is a way to do this, although I'm not liking where this is going... What you need to do it capture the registry that is built when it's installed, and run the first time. Then you can use that to "install" the stuff needed for it to run from the external. Additionally, you will need to make sure that the external drive is the same letter for this to work. A good program for this is Regview.
you can capture file and registry or whatever you want. You just need registry. if you can't figure it out, ask...
Then once you have the registry data, all you have to do is connect the drive, and import the settings. Just using the machine keys won't work, as adobe registers in several locations.
on the machine with the freeze, it's possible you would need to import the settings every time. Additionally, you will need admin access I believe to make it work right.