Explorer is what shows all the icons, etc, so if something is happening, then this won't show. Weird though, as it seems like its over working and not completing the task of starting up, so could be an issue with a program or driver. Hopefully the advice above will help
Thoguh try doing this to see if it helps:
Control Alt Delete, and go to the Processes tab. Right click Explorer and select to End task. Then simply wait for it to end and go from the list.
Next go to File, New Task (RUN), and type:
Then press Enter, and hopefully it'll load up with no problems. If it does, it answers the problem and shows the computer is being overworked at bootup and never completing the task to load it for some reason.