When I try to restart my PC (W7 Home Premium), it will close down Windows and save the settings, but after this when the screen goes dark like normally at a shutdown/reboot, it stays dark and the computer doesn't reboot. I have to turn it off manually by holding the power button and then start it up again. There are no errors while booting.
Most likely there is a service that is failing to stop after the video is turned off. Remove all unnecessary peripherals and see if the issue persists. If it does then you may want to go into MS config and see if there are any unknown services that may be running at start up. Also did you install any software, devices, or updates before this occurred? If so you may want to attempt to uninstall it(them) and see if the issue continues. If all else fails try to use system restore to restore the system to a point prior to this occurring.
If you want you may want to try to live-boot an OS like Ubuntu to see if you still have issues in a different OS without having to reinstall your current one. If that seems to work consistently then it is likely not a hardware issue.
80%-90% of the time an issue like this is not directly linked to failing hardware but it is still a possibility so you may want to try memtest or something of the sort to be safe.
If all else fails and ubuntu appears to work then you may be looking at the unfortunate situation where you have to reinstall your OS.
Best of luck and hopefully removing a USB or uninstalling a recent software change fixes it!