Hello and welcome to the forum!
the CRITICAL_PROCESS_DIED bugcheck is almost always a hardware problem and the KERNEL_DATA_INPAGE_ERROR bugcheck is often caused by bad RAM. I agree with you that the most likely cause, and the one you should look at first, is your mismatched RAM. That's definitely where you should start.
I would remove all RAM sticks except one of the 4GB sticks, Windows will just about run in 4GB, at least you will be able to see whether it BSODs. I would first leave the original 4GB stick inserted and remove all the others. If it still BSODs then remove that 4GB stick and replace it with the other 4GB stick. If it still BSODs then remove that stick and replace it with both 2GB sticks - check the manual to be sure they are in the correct slots.
