If you're talking about purely buying hardware it depends. You could run a Java web app for simply the cost of the machines if you decide to use open source software. However you could go with Oracle as your database and Weblogic as your App Server and then pay for it.
But most importantly, you say yourself you're a .net guy - so you'd have to have the intangible cost of however long it would take you to get to the point where you actually know what you are doing with Java. The syntax is very close, sure, but you have to learn which Java frameworks you want to use, which APIs you want to use, how to deploy to whatever App Server you choose, etc.
Joel wrote about this in Language Wars
How do you decide between C#, Java, PHP, and Python? The only real difference is which one you know better. If you have a serious Java guru on your team who has build several large systems successfully with Java, you're going to be a hell of a lot more successful with Java than with C#, not because Java is a better language (it's not, but the differences are too minor to matter) but because he knows it better. Etc.