In Windows XP and Windows Vista default installs, only Administrators users can low level access to CD devices. Unfortunately that kind of access is needed to rip or burn CDs.
If you need to Rip CDs with a non administrator user you must first grant the right to access CDs to all users. FreeRIP offers an easy to use tool to do it. Please follow these steps:
Now FreeRIP would RIP CDs with non-admin users as well.
Please note that you can go back and prevent normal users to low level access CD devices, by followig the same procedure but selecting "Administrators only" checkbox in step 4.