While economic strength has always been important, it has become more important now than it was in the past. I would say this is because war is a much less frequent thing now. This means that a much more common way of exerting influence is through economic means.
You can see this trend in the rise of China's international influence. Although they do have a large military, they have not been involved in any foreign conflicts. Even so, they are a major force right now in foreign policy. This is because they have so much economic power. Any country that wants to trade with them must be sensitive to their wishes. An example of this can be seen in how nations treat the Dalai Lama and Taiwan. No one wants to get too close to these because they know that will make China angry.
Military might is no longer as relevant as it once was. Economic power is much more important in today's more peaceful world.
Economic strength is at least as important, maybe even more important. Nations are currently scraping to pay down deficits, and many of them are not able to keep their military as strong as they would like. The US has much of the latest technology, but can the US afford to keep purchasing this military strength with growing deficits. Much of the current deficit occurred during the Reagan years of military build up, and this now limits what we can do well into the future.
Some nations have more stable financial situations, but do not have the total amount of money necessary, because of their size, to be a real strong military power. Many of the nations that have valuable natural commodities that the world wants, such as oil, precious metals, etc., have acquired a strong standing in the world of foreign relations. The world's nations have to include the wishes of these countries in their policies because of these resources.
He who has the gold rules.
A countries economic strength has always been an important factor in foreign policy decisions. A strong economy gives a country many options when trying to negotiate with a beligerent country or by providing aid to a needy country.
One example is in post WWII Europe and the Marshall Plan. The United States was able to loan the war torn European countries over $12 billion dollars to help rebuild their countries. This was especially important because economic aid was vital to the strenght and security of European countries that had been ravaged by war. The quicker the these countries could recover the safer the world. Including the Unites States who had fought their second world war in Europe.