Bridget, *
ArcGIS for Desktop is distributed by Esri as a self extracting zip. When you launch that program it does exactly what you describe -- it extracts the installer and then offers to run it (actually just a check-box to prevent it from running after extraction).
It only needs to be extracted and run once!
After that you need to run the ArcGIS Administrator dialog to complete activation and authorization.
Answered similar in this thread -- Student Version - ArcGIS Error Message
You may be out of luck with reusing the 180-day EVA code that came with your text. Esri Press | GIS Books & Tutorials - Buy Books Online
They are not intended to be rearmed. But you can go ahead and try to deauthorize from your Desktop install issuing from a command window:
"C:\Program Files (x86)\Common Files\ArcGIS\bin\softwareauthorization.exe" -s -return all
And then try to reuse it on the laptop from the ArcGIS Administrator dialog--Authorize now... wizard.
You might do better to just obtain another EVA authorization code from school, or the 60-day trial authorization from Esri. Or go ahead and purchase your own Home-use seat ArcGIS for Home Use Program | ArcGIS for Desktop Advanced for Personal Use (US$ 100)
Stuart