Technical support, commonly known as "tech support", is the segment of Blizzard responsible for technical issues in their games and cases are usually handled on a game-specific basis.
They can be contacted in US and Oceanic through the following methods: 
Please Contact Blizzard using the information below if you're having trouble with your account.
- Phone Support
- Speak to a live representative 8AM to 8PM Pacific Time, Mon-Fri, except US holidays
- Technical support category on Wowpedia
- World of Warcraft section of the Support page.
- Billing support