Computer Hardware Help → Re: Desktop freezing, BSoDing, and turning off

Though it is far better than it used to be. I really don't recommend using cards from multiple (GPU) vendors they always seem to bump heads somewhere down the line.

I would check your voltage levels when the machine starts to bog down along with processor heat.

Finally be absolutely sure you are using the latest driver from AMD and the nvidia driver is completely removed.

For CPU Core temp seems to be around 68-69C. Voltage is at 1.378.
GPU is around 42C and voltage seems to mostly be at 0.900, but it does go up to 1.2xx from time to time along with an increase in GPU core clock, but it doesn't appear to happen when everything starts freezing. I checked and I do have the nvidia driver removed.

I think Aranarth is on the right path.
Uninstall all drivers. Run CCleaner, both the temp cleaner but more importantly, the registry cleaner and mack sure you save a backup of the reg clean, just as a precaution.
If you want you can also re-seat the 9800 without an ati card, install nvidia again, reboot then uninstall the package, then reboot. Run CCLeaner from piriform, both the cleaner and reg cleaner.
Also uninstall the video card in device manager at this point.
Remove this card then replace it with your 7870.
Check the seating of the card and also your memory sticks too.
Install only the latest ATI drivers package, I know earlier ati diver packs for the latest cards caused some issues and the latest package fixes those. Reboot.
Run memory tests on the RAM using memtest86+ as the BSOD suggests there could be memory issues. If you find there is errors, remove 1 stick at a time till you stop getting errors to find which stick is faulty.

I don't think you need to run video memory tests on a new card but if you still don't see a fix we can look at it too.

Let us know how you go.