Verify Operation Failed and Other Issues

Adobe Reader X 10.1.1 is not working correctly on my computer which is running Windows XP Professional Service Pack 3. I have several symptoms.
1. If I am able to open a pdf file on my hard drive I get this error message:
   “Verify operation failed.”
    I hit OK and can read the document fine.

2. Many pdf files on my hard drive will not open. I get the error message:
   “There was an error opening this document. There was a problem reading this document (57).”
    I doubt the document is corrupt because I can email them to my coworkers and they can open it.

3. I can open any document inside of Internet Explorer 8. I get the error message:
   “There is a problem with Adobe Acrobat/Reader. If it is running, please exit and try again (0:104)”
    It wasn’t running and trying again won’t help. Usually I download the file and try to open it and if I can't I email to a co-worker and continue on. But now I need to fill out a form online that uses a pdf but I can't download it. What can I do now?

I have uninstalled and reinstalled twice with no success.  I suspect the root problem is the “Verify operation failed.”

Any ideas.