I'm unable to reset the list
This can mean anything. Some people do not put the proper dial status in campaign settings, some do not set Y to Reset Lead-Called-Status for this list in LISTS screen, or forget to press SUBMIT, some have corrupted database...What is your case? How would we know if you don't explain what you are exactly doing?!
That part of your post I cannot understand at all:
when I check in a List of Disposition. (VICIDIAL STATUSES WITHIN THIS SYSTEM:)
I can see DELETE infront of it. I tried to Modify it but it does not work.
Where do you see that option DELETE, in which page? What did you try to modify?
Posting a screenshot of the problematic page and explaining your problem in details would greatly improve your chances for an answer in the right direction, eventually also saving time to those people, willing to help you.