Hoping for some advice re intermittent imac shutdown

Hi..
I was hoping I may be able to get some advice..
I have an early 2009 imac.
All was ok but it decided not to start up.
It makes the noise but as its about to start, it shuts down.
I managed to run hardware test and it said all was ok.
I have an old macbook and managed to get it to work in target disk mode but was unsure what to do next..
I suspect the mother board is not working properly.
The graphics and screen seem perfect.. when theres anything on it..
The disc utility tests I did having booted into safe mode said the hard drive was ok too but it wont start up in normal mode..
I was wondering how I can diagnose what the issue is as the disc utility and hardware test both say all is ok..
Its been suggested possible hard drive, graphics card, power supply and motherboard issue..
I managed to reinstall the original os from the original disc and all worked until it was time to start it. Same again, it beeped, but shut down just as it was starting the "welcome to osx 10.5 (Originally came with osx 10.5.6)" process it does when you first start it the first time after installation.
Any help appreciated..

G'day and welcome to the forums.

Always helps if you can provide the operating system. However you have the discs which is great. Pop the disc in, reboot and hold down 'C'. When it opens, if it does, go to Disk Utility and run Repair Disk from there.

I did that...
The os i installed was the original 10.5.6.
but after it finished installing and tried to start, it shut down.
i have since done some digging around.
I can use it in safe mode, but in normal mode it shuts doen within a few mins..
In safe mode, I looked in the log and found the shutdown causes were -128 which apparently negative values are not good.
Unfortunately, this is an unrecognized code so the computer doesnt know why it shut down..
Not much help...
Having researched safe mode, most sources say that it is most likely a 3rd party product of some sort but this canrt be the case as there is nothing installed other that the original os and nothing plugged in other that the original keyboard and mouse.
I was wondering if safe mode disables some parts of the hardware that may be causing the issue... but its difficult finding the right info..
Im done for today but will continue again!
I even tried another mouse but the same results...
Thanks for your reply

If you start your MBP into Target Disk Mode, connect it to the iMac, start the iMac and hold down "option", does the MBP drive show as a bootable option?

It sounds as though there is a hardware issue, and I don't know if the internal drive is part of the problem.

Can you give more info about the MBP? May help for providing a solution.

yes the macbook drive shows as a bootable option although its a different os
The macbook is an intel core duo 2 gig black 80 gig hd. running 10.6.8 ( max it can go i think)
I think it was made around 2006.
I also have a mac mini but no cable to connect that to the firewire 800 port on the imac

farrarr... you have given me an idea ... perhaps along the lies of where your thoughts were going..
I was thinking to install the os on a usb stick and then run it off that.. Would it be fair to say that if it runs ok it may be a hard drive issue?
any flaws with this idea?