Can a modern state be run based on Halacha?

According to the Bostoner Rebbe the answer is no. At a news conference (http://www.nrg.co.il/online/11/ART2/680/325.html?hp=11&cat=1102&loc=8), the Bostoner Rebbe said that "he is afraid of a halachic state".

Here is the full context of his statement:
אני מפחד מהיום שיהיו 61 חברי כנסת, כי אני לא יודע איך ניתן לנהל מדינה עם האחריות של שמירת התורה. לדוגמה, לסגור את שדה התעופה בשבת, בעולם המודרני אני לא יודע איך אפשר לעשות את זה". ובכנות הוסיף ש"ברוך השם שלא באים לשאול אותי שאלות כאלה".

I am afraid of the day when we have 61 MKs because I don't know how you can run a state with the responsibilities of keeping the Torah. For example, shutting down the airport on Shabbos, in the modern world I don't see how you can do that. And in a moment of candour he added "Thank God that no one comes to ask me these types questions"

Unfortunately, this is emblematic of the modern Charedi leadership,  don't deal with the modern world, rather withdraw from it. Don't engage with the world, rather have everyone sit and learn.

The problem is that it puts Torah in a very bad light. The Torah is supposed to be a blueprint for society, and yet the Charedi leadership says that we can't run a modern society based on Torah because we don't have answers. What does that say about the נצחיות of Torah?

This was not always the case, R' Waldenberg (שו"ת ציץ אליעזר) wrote a whole sefer about these issues as well as many teshuvas and R' Sholmo Zalman Auerbach was already available to address these issues.

It's very interesting that the Bostoner Rebbe pointed to closing the airport on Shabbos as a big problem. IMHO, that is the least of our problems. Power generation, police and army activity on Shabbos are much bigger problems. How do you deal with industries (for example Intel's chip factories) which can't be shut down once a week? How would you create a workable justice system given the Torah's rules of evidence? The list goes on and on.

Additionally, there are very serious economic issues to be dealt with. Modern economies are based on credit and interest, for example, every modern state sells government bonds which pay interest. What about the prohibition of ריבית? How do you square advertising with the prohibitions of אונאת דברים?

To their credit the RZ Rabbis are trying to deal with these issues. To their credit they are publishing seforim which focus on halacha in the modern world, dealing with issues like the army, police, economic issues, etc.