PCI is the older standard, and I only see PCI-express slots on your motherboard anyway.
Yes, looks like you have plenty of room.
Just to make sure, it's not 100% that my problem is hardware related? Correct?
No, not 100%. But after trying two different OS's and getting the same speeds certainly seems to point there. That's why I asked if you could get hold of a NIC just for testing.
You might check if there are any small computer repair shops in your area. I've got a few around me where I could pick up a used NIC for about $2 or $3.