I'm assuming that you installed the 64 bit version of both SuSE and Fedora, if not I would say start there.
Assuming that is not the issue I would turn to looking up your hardware in SuSE's hardware
Support Database
Which shows me one issue
Vendor Device Level of Support
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Gigabyte K8VT800 Partially
I've come to realize that when a piece of hardware is listed as being only partially supported in the Hardware DB it usually means that it is going to take a great deal of work on your part to get it to work properly (if at all). I am not sure if there is a Hardware DB for Fedora but you should definitely look into it. Most people that have tried multiple disto's seem to agree that SuSE and Ubuntu have the best Hardware support and since SuSE 9.3 is such a recent release I would imagine that you will find that your MoBo is only partially supported under Fedora as well.
And you Radeon 9600 also stands out to me. ATI video cards do not have the best support in Linux, I've heard that it has gotten better but they can still be a pain to get set up properly. If you have not installed the 3D drivers (this also includes direct rendering) for your ATI card than if you system trys to run any program that requires those drivers it can severely slow it down or crash it, some of the screen savers that come with SuSE require direct rendering support and if you have not chosen a screen saver SuSE also defaults to randomly choosing one when the screen saver starts.
Also what type of programs are you running when the crashes happen, it could also be that the programs you run use a common library that is partially/fully corrupted, and as soon as the program calls for that library you have a crash.