IMac Crashing; No Fixes Working/Getting a Chance to Work

Question

Hi, this is my first time on these forums asking a question, so forgive me if I've categorised this wrong or something.
I use my iMac nearly everyday for browsing the Internet, word prossessing, digital drawing and playing Minecraft. So, personally, I don't think it is ever being put to degree of stress because I've been doing those same tasks on it for well over a year and it has run smoothly and given me no trouble. However, two days ago, I logged in and got a finder error message, which although I found odd, I simply okayed, not really taking a note of it as I in no way expected  crashing issues to arise from it. The error code started with something like -108, which I now believe was the code -10810.
So I continued using the computer after I okayed the message, only to find that Skype (which automatically opens at login) quit unexpectedly. After clicking the "reopen" button on the report,  the Skype icon bounced once, the blue light underneath appearing for a second. After this I noticed the finder report and clicked it's "reopen" button and thought it didn't work as the report was still there, but it was in fact a second report as every time I tired to open finder, I would receive a new report in mere mili-seconds. I tried other programs such as Safari and Minecraft and they all wouldn't open. Then I went to restart the computer when I noticed the Apple icon and toolbar missing. So I shut down the computer using the power button.
On reboot, things started going crazy. Booting took a while, when it loaded the desktop, it would fade to blue for a few seconds then fade back to the desktop. After a few minutes, the dark, transparent curtain moved down the screen and the message "You have to restart your computer" appeared.
I've tried numerous times to find out the problem/fix it but nothing seems to be working. Worse, the computer either crashes/freezes at login, crashes within seconds of reaching the desktop or works fine (with noticable odd things occurring [such as the screen going blue, desktop items disappearing and then reappearing] but if I try to run things that may help fix my problems (such as software update, reinstalling OS X) the computer crashes/freezes.
What I've tired so far:
The reset (I can't remember the name) where you detach the power cable and hold down the power button for five seconds, then reattach the cable and turn on the computer. No apparent effect.
Safe Mode:
Worked first time, however it crashed while on the desktop on second and third use, after which I haven't used it.
Single-User Mode for fsck:
fsck ran fine, reporting that it did alter something and I had hoped that this had fixed it, but as soon as I reached the desktop, the iMac crashed.
Software Update:
My Internet is bad enough as it is (less than 1MB/Sec, problem with living in a rural area and being on a contract until October) so I haven't been keeping up with some updates as it takes forever to download them. However,  anytime I try to update now, the computer either crashes, won't open Software Update or freezes while it goes to install the updates.
Disk Utility:
Found nothing wrong.
Reinstalling Mac OSX: (Via holding down C at bootup and from the disk if I reach the desktop.)
Either the computer freezes on the Apple logo and spinning gear (which usually doesn't even appear whenever I booted up the iMac) when I hold down C, or it will freeze/crash as the computer tries to restart opening the utilities panel if I run the reinstall from the desktop.
Everytime I've tried to boot the computer today (day three) has resulted in the computer staying on the Apple logo and spinning gear. So without going any further, I decided to ask this to the community because nothing seems to be working, worse being the fact that I'm just on my holidays from University and I'm pretty much lost without the computer
As for the iMac's details I'm really not sure since I generally use the "About this Mac..." feature which I can't get to now. Although I think the only important bits is that it is running on OSX Snow Leopard 10.6.8 with no external hard drives.
I'd really appretiate any help, thanks
Aletonum

Answer 1

One of the memory cards was indeed faulty, and the other completely fine
Thanks very much for all your help!
Although there is one little thing that I've noticed. The iMac works properly, but I tried to software update to see if that may help my Minecraft sound issue (as I still don't think only having 2GB instead of 4GB would cause such a problem) but the software update application won't work. Running the "Software Update" from the apple menu on the toolbar gains no response, nothing happens. If I run the software update from  system preferences, the application icon appears for a second, then disappears (as in the blank app. icon, the blank canvas with the pencil, pen and ruler in the bottom right corner). It does this every time I try to run it. It did work when the computer was crashing, but this started when on one of the occasions I ran the app. while it was crashing. Since this occured during the crashes, and still occurs now, I'm wondering did something simlar happen minecraft, as it's sound disappeared during the crashes and is still gone now.
However, the computer is now working again without crashes, which is the main thing, thanks for helping me fix the issue
Edit: I would mark the topic as solved, but I'm unsure if this would lock the topic or something simlar, so I'd rather leave it open for any ideas regarding the software update and Minecraft issues I'm having