Yes, you can keep the old system running until you are comfortable and sure everything has migrated over successfully to the new computer.
You can use Windows Easy Transfer to migrate over your personal files and settings:
http://www.notebooks.com/2009/10/07/using-windows-easy-transfer-in-windows-7/
Your applications will need to be reinstalled. Once everything has been setup and you are satisfied, you can proceed to decommission the old system.