There are lots of companies that need people who can solve hard (but not always well defined) problems, and being a programmer is certainly a plus. E.g. check out companies that are famous for effectively applying both, e.g. Wal-Mart and Amazon.com (seriously, the latter poaches from the former); prior to the financial industry meltdown, that would have been a place to look into (e.g. many MIT EECS grads used to go there first).

If you're good at problem solving and passable at putting it into code (hey, others can clean that up if need be), you ought to be able to find a niche. Maybe first think about the sorts of problems you like to solve?