I personally have never gone through the process of closing an account, so don't know if there are any particular nuances to it, but if it doesn't seem to be working from the help pages, I'd probably try it from the account itself (possibly also after clearing cache and cookies, or from a different browser, sometimes eBay gets confused about which account is actually logged in).

If you click on Account in My eBay, at the top right should be a 'Close My Account' link which will hopefully work - I haven't seen or heard anyone mention having to get CS involved in the process, at any rate.