Switching pc is not enough, if you are just doing it at home. At least for me, what I did was VPN to my workplace, and then upgrade my last 2 accounts from there (means I have a completely different public IP)

There is no reason you should have to buy new keys, unless the keys already are in use (if you bought them online yourself, that is however very unlikely)

If you can't upgrade them from a secondary location, I'd really suggest calling their customer support, I've heard that they are able to solve this quite fast.

/Mwu