Ebay has done TV campaigns. Here is a link to an older advertisement. http://www.youtube.com/watch?v=h7oq26R6Kak
And more recently, they’ve launched a new campaign aimed at driving mobile users to the site. Here’s a news article with details. http://www.ecommercebytes.com/C/abblog/blog.pl?/pl/2011/9/1316057343.html
To get more to the root of your concern, it seems you feel Ebay isn’t doing enough to drive traffic. To answer that keep in mind that Alexa currently ranks them at 23. http://www.alexa.com/siteinfo/ebay.com
In other words only 22 websites in the entire world are more visited. Most of the top 22 above Ebay are Google properties and Yahoo/Microsoft properties. All in all, being ranked 23rd in the world means they are receiving vast amounts of visits daily.
Ebay drives traffic in many different ways. TV is one that’s already been mentioned, but they’ve also done radio commercials. http://ebayinkblog.com/2008/11/26/ebay-advertising-pr/
Also a lot of traffic comes in organically from various search engines, and they have a large affiliate program as well. Over 220,000 websites have links pointing to some part of ebay.com.