Generally the licence on MSO Home & Student 2010 is for the original machine only…. but do check the EULA and any printed material you may have received with your software
Microsoft responded positively to widespread comment and relaxed the licencing somewhat for the 2013 version (but not as far as I know for the 2010 version.
You could always try it and see how you get on, perhaps giving Dell or Microsoft a ring first to see what the current situation is, in your jurisdiction.