If you renamed it and then deleted it then it can’t be that which is responsible for the sound. More likely to have been the windows sounds that you mentioned, but what is the question.
There is under the Windows sounds, Default Ding (Ding.wav) that would appear to be what you heard “I hear a ding sound.”
I have no idea where your Avast sounds have gone from the list, perhaps if you disable them they aren’t on the list, just checked that and they still appear on my list (XP Pro). From the things that have been happening there does appear to be a problem in the Windows ‘Sounds and Audio Devices’ Properties.