Ok, this is partly not so serious. Please find the serious part below.
What is the best way to start breaking this situation?
Not breaking it at all because you don't have an obvious reason. You just feel ideologically obliged to do it. Well, that's your thing and I can't stop you from it. Break it by choosing any other platform of choice.
Should I migrate to the Java platform? (I know it cost me a lot)
Ok, I might get a lot of downvotes for that, and it's surely subjective opinion, but: Java Web Development is a major pain in the ass. Even James Gosling (creator of Java) said, and I cite: "JSF sucks". ASP.NET is much friendlier in my opinion. If you absolutely must use Java, don't use the major frameworks. Use Apache Wicket or something. But for you more important is: Java is property of Oracle now. It's as free as the .NET platform. Sure, there's OpenJDK. But for .NET, there's also Mono.
You should rather ask: Should I switch to develop for the JVM because I want to learn new things, in which case I'd say:
Sure, because it offers a wider variety of languages that run on it, for example the elegant Scala.
Then how can I start?
Grab platform of choice that is to your liking and just start hacking (some people even use LISP for web development, some even use C, why not take Ruby or Python or PHP?)
C# is an amazing language. Some of its features do not exist in Java (LINQ, real generics, async/await, etc.)! How can I get to that?
Java will get Lambdas and Closures with the next version. However, if you want to write programs for the JVM, I'd advice you to use Scala and skip Java. Scala is an amazing language!
If you want to make money with your startup:
Whether you should change platforms or not depends on your customers. Take the platform that you can sell best in your environment. Probably something based on a standard Apache installation or, for corporate environments, something based on Java Application Servers;
If you want to make money by offering your skills in case the startup fails:
Java is never wrong, neither is .NET. Java will be beneficial to know as the Android market grows. Objective C can be sold very well these days, but I think it will decline again (personal opinion).
If you're doing it for because you love technology:
Take something that is closer to the ivory tower, like Scala or Ruby.