I received a response from Parallels Support. I followed these instructions to the letter. It took about 40 minutes to complete. So far, so good ...
Hello Scott,
Thank you for contacting Parallels Technical Support.
As I understand the issue you are experiencing is regarding the prl_disp_service is consuming 99% CPU in Mac.
To fix the issue we have to uninstall Paralles Desktop completely and reinstall it back.
Please follow the steps given below:
1. Shut down Windows
2. Quit Parallels Desktop
3. Back up your Windows virtual machine by copying the Windows 7.pvm file from Documents=> Parallels folder and pasting it on the Mac desktop screen(or in an external hard drive if you do not have enough available space in Mac HD)
4. Follow the steps suggested in the following article:
http://kb.parallels.com/en/9087
Note: After you enter the first command, it will prompt you to type in the Mac password. So, just type the password and press 'Enter', you will not be able to see the cursor moving or anything getting typed.
5. Once all commands are typed, Quit all applications running in Mac
6. Restart Mac
7. Launch Safari/Firefox
8. Copy and paste the following web link in it:
http://www.parallels.com/download/desktop/
9. Click on 'Download Trial'
Note: the installation file for the trial and the full version is exactly the same
10. Enter your email address and click on 'Proceed to Download'
Note: You will receive a trial activation key in this email address, please ignore it, we do not need it.
11. Click on 'Download your trial software'
12. It will start downloading now
13. Once done, click on the downloaded file, you will get options- 'Install' and 'Uninstall' and 'Getting Started'
14. Click on 'Install'
15. Proceed with the Install wizard
16. Once it is installed successfully, click on 'Close'
17. After this, do not start your Parallels Desktop
18. Go to Finder(first icon on your Dock) => Documents => Parallels => Windows 7.pvm => Double click on it, that will start your Windows.
19. Once the Windows starts for the first time, installation of Parallel Tools will start automatically and your Windows will again restart after it's installation. Sometimes Parallels Tools gets installed along with the Windows installation, so you might not be able to see the Parallels Tools installation.
20. Right click(Ctrl+Click) on the Windows 7 .pvm that you have just backed up on the desktop screen => Click on 'Move to Trash'
Please let us know if the above mentioned steps does not resolve the issue.