Somehow I managed to get MAC pc OS 10.5.3. I have installed mono, monodevelop and monoTouch in that system. I have created a solution and tried to build it simply. But it is showing an error message that "C# compiler crashes". What does that mean and how to resolve that problem. I have tried installing all the software once again, but couldn't found any appropriate thread to it.
You need to provide more details about the crash but I'd venture to guess that your problem stems from not having the latest Xcode and SDKs installed. You need to be running the latest Xcode release (3.2.5 currently) to use the latest MonoTouch (3.2.3 currently) and Xcode 3.2.X requires an Intel-based Mac running Mac OS X Snow Leopard version 10.6.4 or later.
I am not sure what you mean by "somehow I managed to get MAC pc OS 10.5.3" but if that means that you've put together a hackintosh with a 10.5.3 image of OS X and you are trying to run MonoTouch on it, then you're swimming in unsupported waters. There have been reports that the simulator works fine on a hackintosh but you won't be able to deploy to the device.