Spinning Beach Ball of Death & Can't Reinstall OS X

Hi. I am typing this from a laptop. I have a Mac desktop computer that I bought second-hand almost a year ago. The model was made in early 2008 and has 2GB of RAM. The operating software version is 10.8.4 Mountain Lion OS X.

This computer worked perfectly fine until about a week ago when I started getting the spinning beach ball showing up on my screen regularly. Eventually it freezes the whole screen of my computer and the only remedy is to force shut down my computer by holding the power button on the back. Then I have to turn my computer on, but after hearing the startup chime, it gets stuck on that white loading screen and then eventually gets stuck on the screen with the apple logo itself. I then repeatedly turned my computer off an on and had to wait for two or three hours before I can successfully boot up my computer. After successfully restarting my computer, this problem was still recurring.

I believe this is a hardware problem because the spinning beach ball shows up continuously in all of my applications.

Firstly, I removed Google Chrome browser and tried using Safari and then Firefox, but this did not solve my problem.

Next, I opened Activity Monitor and tried to identify any CPU resource hogs, which there were none. They were all below 10%.

I checked CPU in Activity Monitor and the green User percentage remained low while the black Idle percentage remained high.

I then looked at system memory in Activity Monitor and the amount of green free space on the pie chart decreased over time after the desktop computer had been turned on and was dominated by the blue inactive space on the pie chart. However, the amount of page outs I had before my computer froze was less than 10% of the amount of page ins.There was also no swap used.

After that, I went to Disk Usage and to my surpirse I had over 171 GB space free out of 380. The next thing I did was viewed all of my files and deleted 22 files that used over 500 MB on my computer so I then had 284 GB space free. Unfortunately, this still did not help my spinning beach ball problem.

I tried shutting down my desktop computer and booted up in safe mode, but still received the spinning wait cursor.

I have also tried verifying and reparing the disk permissions and then verifying and repairing this disk but this did not work.

I then backed up all my files on the desktop elsewhere and then tried zeroing out all data on my disk and then erased all of my files on my disk. This did not fix the problem.

So now I have to reinstall OS X Mountain Lion, but every time I try to do it says something like "OS X cannot be reinstalled because you aren't connected to the Internet." I had an ethernet cable plugged into the desktop from the router, but my computer fails to recognise that I am actually connected to the Internet. I tried unplugging the cable from both sides and then plugging it in, but this did not work. I changed the location from U.S. to Australia because that's where I live and then tried connecting the computer to the Internet via Wi-Fi. Even though it said I was connected to my wireless network with a black wireless signal figure displayed on the top right of the screen, the same message still appeared.

Prior to doing this, I checked if I had Auto Proxy Server disabled which I had. However, I have DHCP disabled on the desktop computer because it kept giving me IP address conflicts between my devices connected to the network.

I read that I need to have DHCP enabled on the desktop computer, but how can I change this setting on my desktop computer before reinstalling the OS X?

Other questions that I have are:

What caused this Spinning Beach Ball of Death to occur in the first place if this is most likely a hardware problem?

How can I prevent the Spinning Beach Ball of Death from happening again in the future?

Any help would be much appreciated, thanks.