Prompted for Symantec keychain password relentlessly in snow leopard

I just migrated from one Mac to a new Mac (also 10.4.11 to 10.6.1). I think that the updates and protection are working ok, but I’m not entirely sure. Several times a day I get a dozen prompts, one right after the other, for a password for the Symantec keychain. I didn’t create the keychain–I tried following Apple help info on keychains and deleted one labeled Symantec, but it keeps right on prompting me.  I’ve tried every password I can think of that I’ve used for anything. It’s extremely annoying. How can I fix this?  Thanks.