Computer won't restart properly

So I'd really like to upgrade to windows 10, but there's one issue that I'd like to fix before I do because I think it could be harmful to the installation. I know that during the installation of an OS, the computer restarts several times and my computer has not been restarting properly.

When I ask the computer to restart, everything looks like it's going ok. I get a message that the computer is shutting down and then the monitor goes blank and tells me there's no signal from the PC exactly like it should... But the PC just keeps running. I can still hear all the fans moving inside and the computer doesn't quite ever shut down completely and restart. I have to do a hard shut down and then turn it back on.

I've left it like that for a while because I couldn't figure out what to do to fix it, but now I really want to before I install windows 10, so any advice would be much appreciated! Thank you!

Tech Support Guy System Info Utility version 1.0.0.2
OS Version: Microsoft Windows 8.1, 64 bit
Processor: Intel(R) Core(TM) i3-4150 CPU @ 3.50GHz, Intel64 Family 6 Model 60 Stepping 3
Processor Count: 4
RAM: 8135 Mb
Graphics Card: NVIDIA GeForce GTX 580, 1536 Mb
Hard Drives: C: Total - 1430696 MB, Free - 834162 MB;
Motherboard: MSI, Z87-G41 PC Mate(MS-7850)
Antivirus: Windows Defender, Disabled