Random crashes, unable to detect harddrive for a few hours after crash

Summary of symptoms:

• Constant loud fan (starts after around half an hour after boot and does not stop)
• Overheating (not so serious after starting to boot from external hdd)
• Random crashes (usually when running demanding apps)
• Random black screens + crash (usually when playing video, not happened since booting from external hdd + added RAM to 4GB)
• Question mark folder every time after crash (but will be able to reboot after leaving it for a few hours)
• Cannot boot from install DVD after crash (booted and ran for 5 mins then it crashed, 2nd time, black screen and disk keeps running)
• Cannot wake from sleep (need to shut down using power button)

Tried:

• Adding RAM - some help (as above and below)
• Reinstalling OSX - no help
• Repairing permissions - some help (as above and below)
• Checked HDD w/ disk utility and disk warrior - no problem detected
• Booting from external hdd - some help (as above and below)

The story:

I first noticed the problem with my iMac (early 2008, 20", 2.66Ghz C2D, 4gb RAM) when it couldnt wake from sleep. I used to put it to sleep every night (and use it as my alarm clock) I will shut it down when I go to work but I would forget every now and then. Could I have fried the logic board by constantly keeping it on? I started to notice it heating up and the fan running wild in the summer.

It really hit me when it crashed while I was using Garageband a few months ago. The iMac was boiling hot at the top left corner. After a couple of crashes (I had to shut it down by holding the power button), it gave me the question mark folder at start up.

I thought it was dead because I couldnt even boot from install DVD to repair permissions. but when I tried my luck after an hour, it came back on and I could back everything up, repaired permissions, checked disk, did a quick disk defragmentation etc.

The next day the same thing happened again. Thank God it did let me to finish up my project. Then I didnt use garageband and thought it would not crash again.

Then it started to give me sudden black screens (when i was watch videos - youtube or simply playing video files) forcing me to shut it down using the power button every time (no response, cannot use shortcut to shut down).

Every time i force shut it down, it will give me the question mark folder for a few hours. Repairng permissions will make it last longer before the next crash, but it does not solve the problem.

I used to use cleanmymac but heard that it will corrupt the systm. So i tried reinstalling OSX again. Didnt help. Crashes again when I tried to run bigger programs (iphoto, microsoft office ...)

Then I decided to add more RAM. Upgraded from 2GB to 4GB. Did make it last longer before crashing on me again, black screen and all.

I couldnt stand having to wait a few hours before I could boot my computer again so I installed OSX on an external hdd and booted from there.

Thought everything was fine. But the next day when I was using word it gave me the spinning beachball for around half an hour (no black screen), and when I tried to record more tracks on Garageband one day, it crashed on me again. Not sure if it could be due to the speed of the usb port / speed of the external hdd.

With my external hdd, I don't have to wait for a few hours for a reboot after a crash. My iMac can detect the external hdd fine even after it crashes. But the internal hdd will disappear for a few hours after a crash and reboot.

Sound like a logic board issue? Will it help if I replace the internal HDD?

Any help will be much appreciated!!