The first step for anyone who wants to register a trademark is to check the USPTO site (click "Trademarks," then "Search TM database"). For example, if you searched for "NOR CAL," "NORCAL" and "NOR*CAL," you will find there are over 20 registered trademarks for goods and services such as building materials, real estate listings, spring water, recycling services, insurance services, tennis goods, decals, t-shirts (see above), and snowboards. In general, under trademark law you can stop someone from using a confusingly similar trademark. So, for example, if you acquired NOR CAL for one product, you could prohibit someone from using NORCAL or NOR*CAL on similar goods. Your challenge in registering NOR CAL is to find goods or services that are not currently sold under a NOR CAL trademark.
One other wrinkle: Since NOR CAL is a designation for Northern California, you would also want to be sure to follow the rules for trademarks that serve as geographic indications -- in particular, you don't want to imply that your goods come from Northern California if they don't.