How transferrable are programming skills between languages?

A good programmer can easily transfer between languages.

However, the catch is that a good programmer, by definition, is someone who has the skills to use a variety of languages already. If you are hiring someone that only has experience in a single language and programming environment (compiler, framework, etc) then they may not have the necessary experience, especially given that the PHP 'stack' is somewhat different to .NET.

If, however, you are hiring someone who knows Java, PHP and has some experience with Python, then this indicates they have a good range of programming experience already and it's much more likely their skills will transfer easily to ASP.NET.

That is my opinion.

Very transferrable. For a good programmer, syntax is trivial, as long as they know where and when certain design patterns and problem solving techniques should be used (And when they are available for a language), then there should be no reason they shouldn't be considered.

Absolutely. General programming skills are the core value for any developer. In fact, communication skills may even outweigh everything else. A good programmer is a good communicator.

Programming should be about communicating as code will spend more time being looked at and being modified than it will take to write it the first time around, so it better communicate what it is supposed to be doing.

A programmer that has a solid foundation in programming fundamentals should be able to come up to speed reasonably quickly in almost any language.