The VGA->DVI adapter works because DVI supports analog signals. It is possible to send the same signals that are in a VGA connector over a DVI connector.
The DVI->HDMI adapter works because HDMI supports Digital DVI signalling. It is possible to send a Digital DVI signal over HDMI.
Basically, the DVI->HDMI adapter requires digital information from the DVI plug but there isn't any so you don't get any output.
If you want to get a HDMI output from a VGA source you'll need a device designed to do so. They usually consist of a powered box with the discrete logic necessary to digitize the analog VGA signal, allowing you to plug the VGA input on one side and then connect the HDMI output to your device.