How did Islam manage to win converts ? Why did the Iranians, Pakistanis, Indonesians convert to Islam?

I've been to Malaysia several times and I get no sense that the country is turning its back on its past. Bahasa Malaysia, the national language, is more prevalent now than it was when I first visited there 30 years ago. What I see is a country combining its old heritage with the religion it embraced 600 years ago, along with the residual impact of 200 years of British influence and rule. All in all Malaysia is a very mixed bag, which is why I like it so much..