Is there any easy way to identify a hardware problem?

Over the past couple months, my computer has been doing some weird things and I believe it's because of some part of my hardware malfunctioning.

I've had a couple of noticable issues.

1.) My computer has gotten noticeably louder when I play games such as Starcraft 2/Dota 2/Skyrim on ultra settings. Normally I could run these np, but lately my fans are just getting really loud. It's probably just dust, but I'm not sure.

2.) Sometimes my computer will just turn off. It'll turn off and reboot by it's self. Occasionally, when it just suddenly turns off, theres an incredibly high pitch noise, Kind of like that one Crystal Castles song around 0:30.

3.) I had posted about this issue here before, but a month or so ago when I tried to put my computer in sleep mode it would cycle through the lights and sound it makes when it's powering on, but never actually power on. These cycles would last for about 4 seconds, and then happen another 5-6 seconds later. Since then, I do not put my computer in sleep mode.

I'm basically lost when it comes to diagnosing issues hardware related and I'd really really appreciate it if anyone could help me.