I have the same systems (2 of them)
and have not had those issues on one of them.
The other mac developed a faulty mainboard and had
to be replaced and now it has no issues.
I ran tons of tests just like you, have you ran
the system test long and short that boots from
the other disc that comes with os x?
The long test caused a reboot, the short test would
report and error.
what version of os x are you running, you have
to have at least snow leopard 10.6.8