If you check the release notes of 2013 SP1 and the Content Delivery API documentation for 2013 SP1, you will find the following information:
com.tridion.broker.HomeFactory
Deprecated. The Home classes mechanism has been replaced by the Broker Storage Layer API and might be completely removed in future releases. Instead of this class use the StorageManagerFactory class.
com.tridion.broker.components.meta.ComponentMetaHome
Deprecated. The Home classes mechanism has been replaced by the Broker Storage Layer API and might be completely removed in future releases. Instead of this interface use the ItemDAO interface.
So you are encouraged to change your code not using deprecated methods, but that of course does not explain the errors you were seeing on build. My educated guess is that those are coming directly from Eclipse, and the solution for that you can find on Stack Exchange in the answer to this question http://stackoverflow.com/questions/4322893/eclipse-error-the-import-xxx-cannot-be-resolvedhttps://stackoverflow.com/questions/4322893/eclipse-error-the-import-xxx-cannot-be-resolved