When I think of technological innovation, I think of places like Japan or ancient technology, Egypt. I do not believe Israel has ever really been known for their technological advances therefore I do not believe their power and influence is due to those reasons. Quite frankly I don't even consider the country to be powerful or influential.
It could prove to be hard to say for sure why it has such strong historical influence over so many and for so long, but maybe it is because it is considered to be a very holy land to many people as it was the setting for so many holy ancient books.
Israel's historical power and influence were due to communal efforts rather than technological innovation. Israel is a prominent country because so many Jewish people across the world are united in their love for a strong Israel. Donations that span the globe, pro-Jewish cultural organizations, and spiritual unity are what made Israel so powerful and influential.
Israel is nothing without huge amounts of foreign aid from the United States and Europe. Without billions of dollars, the military has no hardware and no soldiers. The Israeli economy can't stand on its own. If the U.S. were to pull its funding, the Israeli military wouldn't be able to withstand attacks from Saudi Arabia or Egypt. Israel doesn't have power and influence because of technology. Their tech comes from foreign aid.
I think that all of the historical power and influence that comes from Israel comes from the religous holy land that they live on, and a lot of other countries want to take over. They are not that advanced in their technology, at least not compared to other world powers.