I have a fairly old computer (uh oh) and I have always been able to run Unity games without any problems. They run perfectly without lag and look great. But when I download the Unity Editor (4.1.2) and I run it, it says I can't run it.

You have to provide some more details, like what's the spces of your comp, what's the error message, etc.

I have a fairly old computer (uh oh) and I have always been able to run Unity games without any problems. They run perfectly without lag and look great. But when I download the Unity Editor (4.1.2) and I run it, it says I can't run it.

The system requirements for the editor may not be the same as for all games made using it. (Also, most Unity games today have been made with far older versions of Unity)