I really think your issue could have been dealt with easily, but you complicated matters by posting the output of fdisk from one machine and then parted from the other. It doesn't matter that they are the same model - they clearly have different hardware configurations. Or are you saying the the first set of outputs from your posts #4 and #6 were from one machine and the outputs in post #8 are from the other? If so, I'm sure we could get to the bottom of this, but we need to know exactly what you are doing and where the outputs are from. I did have a suggestion, but was inhibited from posting it because of the discrepancy between fdisk and parted, and I am still not sure what you are doing.
A few specific comments:
If you do want help, please settle on one and one machine only to work on. There are a few things I would like to check that you can get from either the Mint or the Ubuntu live CD. If we can get you going with one machine, then we can turn our attention to the other, but only after getting the first sorted. If you want to start with the one that is now giving you the Reboot and Select Proper Boot Device error, that's fine.