As your skills are in web site design and computers I would concentrate with that. There is so much money to be made in computing, it is a HUGE business.
Most web sites are simple affairs created with HTML (I assume you are doing simple web sites).
Large companies have more complex websites that use database back ends, and product like MYSQL, PHP, ASP, Java etc.
There is money to be made designing websites, so I would start small, but in the meantime build up your skils in these other technologies, then you will be able to offer a complete web site solution.
Remember Google started only a few years ago as a simple search engine and now look at them.