My colleague is making desperate attempts to get in touch with me regarding an important project and I'm not going to reply.
Is that a good idea? What kind of project is it?
It's a project for a big time client
You should answer their urgent messages because it could be important to the project. If you fail to deliver the project then you may be fired from your job due to neglect.
It's not my fault I am busy with other things.  I don't want to help them out.
Its sounds like it could be really important and might impact your job.  It can be hard trying to juggle a lot of different things but your colleague will appreciate your help and you can help them not be so stressed out, also you could save the day!