I'm thinking of hiring a project manager to lead the development of few web apps my company is doing.
The guy I'm considering has considerable experience in managing projects for a large digital agency. He's quite familiar with all technologies and process, understands programming logic and how to work with people, but he is not a strong programmer himself (apart from 2 year experience with Visual Basic for applications, programming some Access databases).
It is necessary for a project manager to be able to resolve programming problems and speak with developers on a technical level, or not?
I would first ask if you really need a project manager in your startup?
Unless you already have a decent size team, this person will not have much to do purely as a project manager. Ideally, this person can also take on additional work like QA, writing requirements, support, etc...
As for having programming skills, it would definitely be nice. From my experience, I've seen many teams struggling while trying to explain tasks/concepts to a non-tech PM, which will slow you down.