Finding an IP address of a twitter account?

[Nik]

Not really possible for you.

Reason one.
The IP address you seek never conencts to your computer. It connects to Twitter. This means you would have to hack Twitter to get anywhere close to tracking him. Which I don't recommend.

Either that or know how to track a specific computer through a field of billions.

Reason two
His or her IP address may change daily. So by the time you come to tracking it. It has probably changed several dozen times.

I don't know what would be the steps to sorting your problem out. Take documented proof of the harassment and your communication with Twitter. If nothing ever comes of it then try looking for help with the law. Online bullying has had sever consequences in the past maybe you could look at Twitters terms of use. If there is anything in there regarding language or attitude and these people are breaking it and Twitter is doing nothing about it. Twitter is essentially breaking their own terms of use.