Is it really against the law to use this version on your business computer?
Yes. As soon as you install it it sends your IP address to Microsoft who then contact your local police force.
The Microsoft wesite has a small blurb stating who is allowed to buy the student/teacher version of Office. Basically you need to be enrolled in some kind of educational course. Now there is absolutely no reason why you could not both run, or work for, a business and be enrolled in a course.
Provided you limit your installations to those stated in the end user agreement (three concurrent installations if I remember correctly,) and you bought it while enrolled in an educational course, you can install on whatever computer you like.
It would be a violation of the license agreement. Now I can’t find the text of the license agreement itself, but did find this from the FAQ for the product:
How irritating. Home & Student has all I need, I dont need the extra stuff on Small Business.
There’s legal and there’s “legal.” If I were you, I wouldn’t lose sleep over this one. The key point for Microsoft is that they got something out of you rather than you simply loading a pirated copy you picked up somewhere.