ISTANBUL—For years now Turkey has been talked of as being on the cusp of an Internet boom, but has reality hit? Startups are closing, investment remains scarce and the changing political climate in the country has, according to expatriate Turks, made it less attractive to those thinking of coming home to build a company.

On paper Turkey has a lot going for it. According to the International Telecommunication Union, it hosts Europe's fifth-largest online population, after Russia, Germany, the U.K. and France. Credit-card penetration,...