The IP address identifies the sender in relativey few cases. Most posters have dynamic addresses assigned by their ISPs when they log on. In that same vein, however, you WOULD certainly be able to identify the ISP, and inform them that one of their members was playing dirty.
Save all your messages for evidence. Most eMail clients have a function to display all the routing steps a message has taken. In Eudora, it's called "Blah, Blah", and the option is usually defaulted to "OFF" so you don't see all that garbage.
In the meantime, definitely delete, definitely ignore. Only a certified sicko would persist if he wasn't getting feedback.