Yes that is correct, the key for starter only works for starter. you should be able to install starter edition again and use the key, or you could reinstall using a recovery disk. If you have one you could follow this procedure:
1. Press the power button to turn the system on.
2. Select to boot from a USB optical drive. There are two ways to do this:
2.1. Press <F2> during the Power-On Self-Test (when the Acer logo is displayed onscreen after bootup) to enter BIOS Setup.
2.1.1. Select the Boot menu.
2.1.2. Refer to onscreen instructions to set the first device to any bootable optical disc drive.
2.2. Press <F12> during the Power-On Self-Test (when the Acer logo is displayed onscreen after bootup), and select the USB ODD from the list that appears.
3. Ensure the Recovery disc is in an external (USB) optical disc drive, and exit the boot selection menu, by selecting Exit Saving Changes from the Exit menu or pressing <F10>, or by pressing <Enter> as appropriate.
4. Select Exit Saving Changes from the Exit menu or press <F10>.
5. Follow the on-screen instructions to complete the installation process.
6. When you finish the recovery process, please remove the Recovery disc and insert the System disc again.
7. Restart your computer.