boot - Windows 7 computer freezes shortly after startup, then won't sart up for some time (hardware related)

I've had some really strange, but until now, rare problems with my Windows 7 PC. A few minutes after startup, the computer froze, as in the displayed frame stayed the same and the computer did not respond to any keyboard and mouse inputs; no bluescreen (typically, but sometimes I've had bluescreen scrashes).

The pattern is pretty consistent:

• the computer freezes after a somewhat random amount of time after booting


• it never freezes a few hours into being booted


• one time it even seemed to freeze on the Windows loading screen


• one time the motherboard output a constant, loud beeping noise after booting and login (might be unrelated)

Lately, after startup, I couldn't even get the computer to boot at all. No screen output, no motherboard-beeping signals, simply nothing. One time my computer froze on the Windows loading screen.

Here's a short summary of all the problems:

• seemingly random computer freezes, always shortly after booting


• after turning power off and rebooting, computer starts and either:
  
  
  
  • the computer is stuck on a black screen with nothing happening
  
  
  • the computer starts and no problems occur
  
  
  • the computer starts but it freezes again shorty after booting
  
  

I am fairly certain that this must be a hardware related issue, I just can't nail it down to a specific component. My PC is really old (6-7?), except for a new GTX 960 which I have purchased 2 years ago.

Any help would be appreciated a lot. Thanks in advance!