It sounds like you are attempting to stream videos with the Library Server. When you are trying to stream videos, depending on the source type, it can take a very long time (for example, a H264 compressed 720p MKV will take a LONG time unless you have a very powerful serving machine). The system essentially has to transcode from the source format to a format appropriate for streaming. The time this takes depends on the speed and capabilities of the computer running the library server. It doesn't work properly with all source file types.
If the laptop has the source filesystem mounted as a network drive, and can access the files via the same path, then it should play basically just like it does locally. That's probably your best bet if you want to watch videos from the laptop that live on the desktop system.
The streaming system is really designed to allow you to stream out over the Internet. If you are on a LAN, you'll get much better performance and reliability (not to mention quality and speed) by accessing the files directly.