If your OS and your machine don't meet the minimum requirements for the program, no matter who develops the app, you can't use it. It's always been that way.
Sounds like you have a 32 bit operating system or an incompatible processor. You can use earlier versions of AE. Let us know what kind of machine you have and what operating system you have and we can possibly point you to a version of AE that will work.
I've run AE on Toshiba laptops before. It has nothing to do with the brand, it has to do with the system specs.
You can't have a VW Golf tow a space shuttle.