I can't select a class or batch to participate in the event.

The reason you can’t select a Class or a batch can be one of two things: 
1. That specific distance or batch you are selecting is full.
2. You are not fulfilling the required Batch/Class criteria, this means that you are trying to enter a Class or batch that have specific rules for entering. This can be a specific age category, or team criteria. Some Classes require you to be entered into a team of let's say 4 members and you will not be able to enter the class untill you are part of a team that concists of 4 members. 
In this case, go back to the previous page and add a team with the specified number of members in it. More on teams here (Add a team during the registration process)